'use strict';var _Mathsign=Math.sign,_MathPI=Math.PI,_NumberisInteger=Number.isInteger,_Mathabs=Math.abs,_Mathexp=Math.exp,_Mathlog=Math.log,_Mathsqrt=Math.sqrt,_Mathpow=Math.pow,_Mathround=Math.round,_Mathfloor=Math.floor,Statistics=function(o,l,u={}){this.data=void 0,this.columns=void 0,this.valueMaps=void 0,this.storedResults=void 0,this.lastUpdated=void 0,this.validScales=['nominal','ordinal','interval','metric'],this.zTable=void 0,this.factorials=[1,1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,6227020800,87178291200,1307674368000,20922789888000,355687428096000,6402373705728000,121645100408832000,2432902008176640000,5109094217170944000],this.defaultOptions={epsilon:1e-5,excludeColumns:['ID','id'],incompleteBetaIterations:40,incompleteGammaIterations:80,maxBarnardsN:200,spougeConstant:40,suppressWarnings:!1,zTableIterations:25},this.init=function(M,S,T={}){for(var C in'undefined'==typeof M&&this.errorMessage('No data was supplied.'),this.defaultOptions){var N='object'==typeof T&&this.has(T,C)&&this.has(this.defaultOptions,C)?T[C]:this.defaultOptions[C];Object.defineProperty(this,C,{value:N,writable:!1})}return'undefined'!=typeof M&&this.updateData(M,S),this},this.updateData=function(M,S){this.addData(M),'object'==typeof S&&this.assignValueMap(S),M.constructor===Array&&'object'!=typeof S&&(this.errorMessage('It is strongly encouraged to initalise statistics.js with a variable table that defines the scale of measurement of each variable (e.g. nominal, metric.). All variables will be assumed as nominal and subsequent analyses will likely be flawed.'),g.apply(this))},this.addData=function(M){try{let S=typeof M;if('string'!=S&&'object'!=S||null===M)throw'Input variable data is neither an object nor a JSON encoded string. The variable type is '+S+'. The data could not be properly imported.';return'string'==S&&(M=JSON.parse(M)),this.data=this.data?this.data.concat(M):M,this.lastUpdated=Date.now(),!0}catch(S){return this.errorMessage(S)}},this.addRow=function(M){if('undefined'==typeof M)return this.errorMessage('Add Row: No data was given.');let S='undefined'==typeof this.data?[]:this.data;return S.push(M),this.data=S,this.lastUpdated=Date.now(),!0},this.removeRow=function(M,S=!1){if('undefined'==typeof M)return this.errorMessage('Remove row: No index was given.');let T=this.data,C=this.has(this.columns,'id')||this.has(this.columns,'ID');if(S&&C){let N=-1,I=0;for(;-1==N&&I<T.length;)(this.has(T[I],'id')&&T[I].id===S||this.has(T[I],'ID')&&T[I].ID===S)&&(N=I);T.splice(I,1)}else{if(S&&!C&&this.errorMessage('Remove row: There is no column "id" or "ID". The index '+M+' will be treated as the number of the row, starting at 0.'),M>T.length-1)return this.errorMessage('Remove row: The stored data has only '+T.length+' rows and index '+M+' is too large. Indexes start at 0.');T.splice(M,1)}return this.data=T,this.lastUpdated=Date.now(),!0},this.reset=function(){try{return this.data=void 0,this.storedResults=void 0,this.lastUpdated=Date.now(),!0}catch(M){this.errorMessage(M.message)}},this.assignValueMap=function(M){let S={},T={};for(var C in M){if(!this.has(M,C)||-1<this.excludeColumns.indexOf(C))continue;let V,N=M[C],I=N;if('object'==typeof N&&this.has(N,'scale')&&(this.has(N,'valueMap')&&(V=N.valueMap),I=N.scale),'undefined'==typeof V&&('nominal'===I||'ordinal'===I)&&(V=this.getUniqueValues(this.data.map((D)=>{return D[C]}))),'undefined'!=typeof V&&(T[C]=V),-1<this.validScales.indexOf(I))S[C]=I;else{S[C]='nominal';let D='"'+I+'" scale for variable "'+C+'" is invalid. It was assumed as nominal. Valid scales of measurement include: '+this.validScales.join(', ');this.errorMessage(D)}}this.columns=S,this.valueMaps=T,this.sanitizeColumns()};var g=function(){let M={},S=['th','st','nd','rd'];for(var T=0;T<this.data.length;T++)if('object'!=typeof this.data[T]){let N=T%100,I=T+(S[(N-20)%10]||S[N]||S[0]);this.errorMessage('The '+I+' row was ignored because it is not an object.')}else for(var C in Object.keys(this.data[T]))!C in M&&(M[C]='nominal');this.columns=M,this.lastUpdated=Date.now()};this.sanitizeColumns=function(){let M=this.columns,S=this.data;for(var T=0;T<S.length;T++){let N=S[T];for(var C in M){let I=N[C],V=I;switch(M[C]){case'metric':V=this.isNumeric(I)?I:NaN;break;case'interval':V=this.isNumeric(I)?I:NaN;break;case'ordinal':if('undefined'!=typeof this.valueMaps){let D=this.valueMaps[C];'undefined'!=typeof D&&(V=D.indexOf(I))}break;default:}S[T][C]=V}}this.data=S,this.lastUpdated=Date.now()},this.setScale=function(M,S){return'undefined'==typeof S?(this.errorMessage('This method needs to be called with valid values for both the variable and the scale of measurement to set.'),!1):this.has(this.columns,M)?-1===this.validScales.indexOf(S)?(this.errorMessage('"'+S+'" is not a valid scale of measurement. Valid scales include: '+this.validScales.join(', ')),!1):(this.columns[M]=S,!0):(this.errorMessage('There is no variable "'+M+'" defined.'),!1)},this.getScale=function(M){if('undefined'!=typeof M&&this.has(this.columns,M))return this.columns[M]},this.getValueMap=function(M){if('undefined'!=typeof M&&this.has(this.columns,M))return this.valueMaps[M]},this.applyValueMap=function(M,S){let T=this.getValueMap(M);if('ordinal'===this.getScale(M)&&'undefined'!=typeof T)return'undefined'===S&&(S=this.getColumn(M)),S.map((C)=>{return T[C]})},this.checkLastUpdated=function(M,S){return''!==M&&this.has(this.columns,M)&&'undefined'!=typeof M&&'undefined'!=typeof S&&('undefined'==typeof this.storedResults||'undefined'==typeof this.storedResults[M]||'undefined'==typeof this.storedResults[M][S]||'undefined'==typeof this.storedResults[M][S].lastUpdated||this.storedResults[M][S].lastUpdated<this.lastUpdated)},this.updateStatistics=function(M,S,T){if('undefined'!=typeof M&&'undefined'!=typeof S&&'undefined'!=typeof T){var C={value:T,lastUpdated:Date.now()};'undefined'==typeof this.storedResults?this.storedResults={column:{parameter:C}}:'undefined'==typeof this.storedResults[M]?this.storedResults[M]={parameter:C}:this.storedResults[M][S]=C}},this.getStatistics=function(M,S){return'undefined'!=typeof M&&'undefined'!=typeof S&&this.has(this.columns,M)&&'undefined'!=typeof this.storedResults[M][S].value?this.storedResults[M][S].value:void 0},this.getColumn=function(M){return'undefined'==typeof M?this.errorMessage('Get column: No column to sort was specified.'):this.has(this.columns,M)?this.data.map((S)=>{return S[M]}):this.errorMessage('Get column: The column "'+M+'" was not found.')},this.sortColumn=function(M,S='asc'){return'undefined'==typeof M?this.errorMessage('Sort column: No column to sort was specified.'):this.has(this.columns,M)?this.sort(this.getColumn(M),S):this.errorMessage('Sort column: The column "'+M+'" was not found.')},this.sortDataByColumn=function(M,{data:S=this.data,order:T='asc',changeOriginal:C=!1}={}){return S!==this.data||'undefined'!=typeof M&&this.has(this.columns,M)?S===this.data||this.has(S[0],M)?function(N,I,V,D){return I.sort(function(F,P){return D.isNumeric(F[N])&&D.isNumeric(P[N])?('asc'===V?1:-1)*(F[N]-P[N]):0})}(M,C?S:this.deepCopy(S),T,this):this.errorMessage('Sort data by column: The column "'+M+'" does not exist.'):this.errorMessage('Sort data by column: No column was specified or this column does not exist.')},this.sort=function(M,S='asc'){return'undefined'==typeof M?this.errorMessage('Sort: No values given.'):M.constructor!==Array||0===M.length?this.errorMessage('Sort: No array or an empty array of values was given.'):function(T,C,N){return T.sort((I,V)=>{return C.isNumeric(I)&&C.isNumeric(V)?('asc'===N?1:-1)*(I-V):0})}(this.deepCopy(M),this,S)},this.getUniqueValues=function(M){if('undefined'==typeof M)return this.errorMessage('Get unique values: No values given.');let S=this.validateInput(M,'nominal','get unique values');return!1===S?void 0:this.sort(S.data.filter((T,C)=>{return S.data.indexOf(T)===C}))},this.reduceToPairs=function(M,S){if('undefined'==typeof S||'undefined'==typeof M)return this.errorMessage('This method requires two variables to be compared.');let T=this.validateInput(M,'nominal');if(!1!==T){let C=this.validateInput(S,'nominal');if(!1!==C){let N=T.length>=C.length?T.length:C.length,I=[],V=[],D=[],F='string'==typeof M?M:'first',P='string'==typeof S?S:'second';for(var B=0;B<N;B++){let U=T.data[B],O=C.data[B];if(void 0!==typeof U&&void 0!==typeof O&&!isNaN(U)&&!isNaN(O)){I.push(U),V.push(O);let R={};R[F]=U,R[P]=O,D.push(R)}}return{length:I.length,missings:N-I.length,valuesFirst:I,valuesSecond:V,valuesCombined:D}}}},this.validateInput=function(M,S='metric',T=''){let C={};if('string'!=typeof M&&(M.constructor!==Array||M.constructor===Array&&0==M.length))return this.errorMessage('No properly formatted data was supplied. Specify a column by its name (string) or supply an array of values.'),!1;if('string'==typeof M&&''!==M)C.data=this.getColumn(M),C.scale=this.getScale(M),C.length=C.data.length;else if(M.constructor===Array&&0<M.length){if(!1===this.validateData(M,S))return!1;C.data=M,C.scale=S,C.length=C.data.length}else return!1;if(0==C.length)return this.errorMessage('The supplied data or the data of the supplied column contains no values.'),!1;if(!h.apply(this,[C.scale,S])){let N=this.validScales.slice(this.validScales.indexOf(S)).join(', '),I=''===T?'This statistical method':T.charAt(0).toUpperCase()+T.slice(1);return I+=' is only defined for these scales of measurement: '+N+'. The scale of the supplied data is '+C.scale+'.',this.errorMessage(I),!1}return C},this.validateData=function(M,S='metric'){if('undefined'==typeof M||o.constructor!==Array)return this.errorMessage('Validate data: Specify an array storing the values to be validated.');if('nominal'===S)return!0;for(var T=0;T<M.length;T++)if(!this.isNumeric(M[T]))return this.errorMessage('Validate data: The supplied data contains non-numeric values: '+M[T]+' at index '+T),!1;return!0},this.isNumeric=function(M){return'undefined'==typeof M?void 0:!Array.isArray(M)&&!isNaN(parseFloat(M))&&isFinite(M)};var h=function(M,S){return this.validScales.indexOf(M)>=this.validScales.indexOf(S)};return this.errorMessage=function(M){if(!this.suppressWarnings)try{throw new TypeError('string'==typeof M?M:M.message)}catch(S){console.error('statistics.js: '+S.message)}},this.has=function(M,S){var T=Object.prototype.hasOwnProperty;return T.call(M,S)},this.deepCopy=function(M){let S=Array.isArray(M)?[]:{};for(let T in M){let C=M[T];S[T]='object'==typeof C?this.deepCopy(C):C}return S},Statistics.prototype.assignRanks=function(M,{data:S=this.data,order:T='asc',handleTiedValues:C='mean',returnFrequencies:N=!1}={}){if('undefined'==typeof M)return this.errorMessage('Assign ranks: You need to specify a column to be ranked.');let I=this.deepCopy(this.sortDataByColumn(M,{data:S,order:T,changeOriginal:!1})),V={};for(var D=0;D<I.length;D++){let U=I[D][M];V[U]=V[U]?V[U]+1:1}let P=0,B=[];for(var D=0;D<I.length;D++){let U=I[D][M],O=D+1;1===V[U]?P=0:'mean'===C?(P++,O=D+V[U]/2-P+1.5):'random'===C&&(0===B.length&&(B=Array.from(Array(V[U]),(G,A)=>A+D+1)),O=B[_Mathfloor(Math.random()*B.length)],B.splice(B.indexOf(O),1)),P==V[U]&&(P=0),I[D]['rank-'+M]=O}return N?{data:I,frequencies:V}:I},Statistics.prototype.contingencyTable=function(M,S){if('undefined'==typeof S)return this.errorMessage('A contingency table requires two columns to analyze.');if(!this.has(this.columns,M))return this.errorMessage('There is no variable "'+M+'" defined.');if(!this.has(this.columns,S))return this.errorMessage('There is no variable "'+S+'" defined.');let T=this.getScale(M),C=this.getScale(S);if('nominal'!==T&&'ordinal'!==T||'nominal'!==C&&'ordinal'!==C)return this.errorMessage('Both variables need to be nominal for. They are '+T+' and '+C+'.');let N=this.getValueMap(M),I=this.getValueMap(S);if('undefined'==typeof N||'undefined'==typeof I)return this.errorMessage('Contingency table: There are no valid values.');let V={total:{total:0}},D=this.data;for(var F=0;F<D.length;F++){let B=D[F][M],U=D[F][S];'undefined'==typeof V[B]&&(V[B]={total:0}),V[B][U]='undefined'==typeof V[B][U]?1:V[B][U]+1,V.total[B]='undefined'==typeof V.total[B]?1:V.total[B]+1,V.total[U]='undefined'==typeof V.total[U]?1:V.total[U]+1,V[B].total++,V.total.total++}let P={detailled:V};return 2>=N.length&&2>=I.length&&(P.a=V[N[0]][I[0]]||0,P.b=V[N[0]][I[1]]||0,P.c=V[N[1]][I[0]]||0,P.d=V[N[1]][I[1]]||0),P},this.showData=function(M){if('string'==typeof M&&this.has(this.columns,M))'ordinal'===this.getScale(M)?console.log(this.applyValueMap(M)):console.log(this.getColumn(M));else if('undefined'==typeof M){let C=this.valueMaps,N=this.data;if('undefined'!=typeof C)for(var S in C)if(this.has(C,S)&&'undefined'!=typeof C[S]&&'ordinal'===this.getScale(S))for(var T=0;T<N.length;T++)N[T][S]=C[S][N[T][S]];console.table(N)}else console.log(M)},this.scatterPlot=function(M=this.data,{canvas:S=null,xAxis:T=null,yAxis:C=null,width:N=null,height:I=null,dotRadius:V=4,showGrid:D=!1,minNumberXMarks:F=8,minNumberYMarks:P=8,background:B='#FFFFFF',dotColor:U='#000000',gridColor:O='#CCCCCC',axisColor:R='#000000'}={}){if('undefined'==typeof M)return this.errorMessage('Scatter plot: No data given.');if(M.constructor!==Array||0===M.length)return this.errorMessage('Scotter plot: Data is not an array or empty.');if(0>=F||0>=P)return this.errorMessage('Scotter plot: The number of line to plot must be larger than 0.');let G=typeof M[0];if('object'==G&&(!T||!C))return this.errorMessage('Scatter plot: The variables for the x and y axes need to be supplied.');let A={},L=Infinity,E=-Infinity,W=Infinity,K=-Infinity,Y=0;for(var X=0;X<M.length;X++){let me,ce,ue=[];if('number'==G||M[0].constructor===Array){if(!this.isNumeric(M[X]))continue;me=X,ce=M[X]}else if('object'==G){if(!this.has(M[X],T)||!this.has(M[X],C)||!this.isNumeric(M[X][T])||!this.isNumeric(M[X][C]))continue;me=M[X][T],ce=M[X][C]}this.has(A,me)?ue=A[me]:Y+=1,ue.push(ce),A[me]=ue,me>E&&(E=me),me<L&&(L=me),ce>K&&(K=ce),ce<W&&(W=ce)}0.1>L/E&&(L=0),0.1>W/K&&(W=0),null===S&&(S=document.createElement('canvas'));let Q=S.getContext('2d'),H=N?0.1*N:0.1*(E-L);for(var J in N=(N?N-2*H:E-L)+2*V,I=(I?I-2*H:K-W)+2*V,400>N&&(N=400),400>I&&(I=400),40>H&&(H=40),S.width=N,S.height=I,Q.fillStyle='transparent',Q.fillRect(0,0,N,I),Q.fillStyle=U,A)for(var Z=0;Z<A[J].length;Z++){let ue=(J-L)*(N-V)/(E-L),me=I-(A[J][Z]-W)*(I-V)/(K-W)-V;Q.fillRect(ue,me,V,V)}const $=function(ue,me,ce,pe,ge,fe=R){ue.strokeStyle=fe,ue.beginPath(),ue.moveTo(_Mathfloor(me),_Mathfloor(ce)),ue.lineTo(_Mathfloor(pe),_Mathfloor(ge)),ue.stroke(),ue.strokeStyle=R};let _=document.createElement('canvas'),ee=_.getContext('2d'),ae=N+2*H-2*V,te=I+2*H-2*V;_.width=ae,_.height=te,ee.fillStyle=B,ee.fillRect(0,0,ae,te),ee.fillStyle=R,ee.font=0.2*H+'px Arial',ee.textAlign='center',ee.textBaseline='middle';let ie=_Mathround((E-L)/F),ne=1<=ie?_Mathpow(10,parseInt(ie).toString().length-1):0.01;ie=_Mathround(ie/ne)*ne;let se=0,re=0,oe=0;if(0<ie)for(var X=0;X<F||se<=E&&re<=N-2*H;X++)se=_Mathround(L/ne)*ne+X*ie,re=0.5*H+(se-L)*(N-V)/(E-L),re>ae-0.5*H||re<0.5*H||($(ee,re,te-0.4*H,re,te-0.6*H),D&&$(ee,re,te-0.6*H,re,0.5*H,O),ee.fillText(se,re,te-0.2*H));let de=(K-W)/P,le=1<=de?_Mathpow(10,parseInt(de).toString().length-1):0.01;if(de=_Mathround(de/le)*le,se=0,0<de)for(var X=0;X<P||se<=K&&oe<=I-2*H;X++)se=_Mathround(W/le)*le+X*de,oe=1.5*H-2*V+I-(se-W)*(I-V)/(K-W),oe>te-0.5*H||oe<0.5*H||($(ee,0.4*H,oe,0.6*H,oe),D&&$(ee,0.6*H,oe,N+H-2*V,oe,O),ee.fillText(se,0.2*H,oe));return $(ee,0.5*H,te-0.5*H,ae-H,te-0.5*H),$(ee,0.5*H,te-0.5*H,0.5*H,0.5*H),ee.drawImage(S,0.5*H-0.5*V,1.5*H-1.5*V),Q.drawImage(_,0,0,N,I),S},this.init(o,l,u)};'undefined'==typeof exports?window.Statistics=Statistics:('undefined'!=typeof module&&module.exports&&(exports=module.exports=Statistics),exports.Statistics=Statistics),Statistics.prototype.mean=function(o){return'undefined'==typeof o?void 0:this.arithmeticMean(o)},Statistics.prototype.arithmeticMean=function(o){if('undefined'==typeof o)return this.errorMessage('Arithmetic mean: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'mean'))return this.getStatistics(o,'mean');let l=this.validateInput(o,'interval','arithmetic mean');if(!1!==l){let u=this.sumExact(l.data)/l.length;return'string'==typeof o&&this.updateStatistics(o,'mean',u),u}},Statistics.prototype.geometricMean=function(o){if('undefined'==typeof o)return this.errorMessage('Geometric mean: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'geometricMean'))return this.getStatistics(o,'geometricMean');let l=this.validateInput(o,'metric','geometric mean');if(!1===l)return;let u,g=!1;return u=l.data.reduce((h,M)=>{return 0<M?h*M:(g=!0,h)},1),!g&&0<l.length?u=_Mathpow(u,1/l.length):(this.errorMessage('Geometric mean is not defined because the data contains non-positive values.'),u=void 0),'string'==typeof o&&this.updateStatistics(o,'geometricMean',u),u},Statistics.prototype.harmonicMean=function(o){if('undefined'==typeof o)return this.errorMessage('Harmonic mean: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'harmonicMean'))return this.getStatistics(o,'harmonicMean');let l=this.validateInput(o,'metric','harmonicMean');if(!1===l)return;let u=!1,g=!1,h=l.data.reduce((M,S)=>{return 0>S?(g=!0,0):0===S?(u=!0,0):M+1/S},0);return h=u?0:l.length/h,h=g?void 0:h,'string'==typeof o&&this.updateStatistics(o,'harmonicMean',h),h},Statistics.prototype.rootMeanSquare=function(o){if('undefined'==typeof o)return this.errorMessage('Root mean square: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'rootMeanSquare'))return this.getStatistics(o,'rootMeanSquare');let l=this.validateInput(o,'interval','root mean square');if(!1!==l){let u=_Mathsqrt(l.data.reduce((g,h)=>{return g+h*h},0)/l.length);return'string'==typeof o&&this.updateStatistics(o,'rootMeanSquare',u),u}},Statistics.prototype.cubicMean=function(o){if('undefined'==typeof o)return this.errorMessage('Cubic mean: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'cubicMean'))return this.getStatistics(o,'cubicMean');let l=this.validateInput(o,'interval','cubic mean');if(!1===l)return;let u=l.data.reduce((g,h)=>{return g+h*h*h},0);return u=0<=u&&0<l.length?_Mathpow(u/l.length,1/3):void 0,'string'==typeof o&&this.updateStatistics(o,'cubicMean',u),u},Statistics.prototype.winsorisedMean=function(o,l=0.2){if('undefined'==typeof o)return this.errorMessage('Winsorised mean: No data was supplied.');if(0>l||0.5<l)return this.errorMessage('winsorisedMean should be called with a percentage value within the range of [0, 0.5].');if(0.5===l)return this.median(o);let u=this.validateInput(o,'interval','Winsorised (truncated) mean');if(!1===u)return;let g=_Mathfloor(u.length*l),h=this.sort(u.data).slice(g,u.length-g);h=Array(g).fill(h[0]).concat(h).concat(Array(g).fill(h[h.length-1]));let M=this.sumExact(h)/u.length;return M},Statistics.prototype.gastwirthCohenMean=function(o,{alpha:l=0.25,lambda:u=0.25}={}){if('undefined'==typeof o)return this.errorMessage('Gastwirth-Cohen mean: No data was supplied.');let g=this.validateInput(o,'ordinal','Gastwirth-Cohen Mean');if(!1===g)return;if(!this.isNumeric(l)||0>l||0.5<l)return this.errorMessage('Gastwirth-Cohen mean should be called with an alpha value within the range of [0, 0.5].');if(!this.isNumeric(u)||0>u||0.5<u)return this.errorMessage('Gastwirth-Cohen mean should be called with a lambda value within the range of [0, 0.5].');let T,h=this.quantile(o,l),M=this.quantile(o,1-l),S=this.median(o);return'undefined'!=typeof h&&'undefined'!=typeof M&&'undefined'!=typeof S&&(T=u*(h+M)+(1-2*u)*S),T},Statistics.prototype.midRange=function(o){if('undefined'==typeof o)return this.errorMessage('Mid-range: No data was supplied.');let l=this.validateInput(o,'interval','mid-range');if(!1!==l){let u=this.minimum(o),g=this.maximum(o);return'undefined'!=typeof u&&'undefined'!=typeof g?0.5*(u+g):void 0}},Statistics.prototype.median=function(o){if('undefined'==typeof o)return this.errorMessage('Median: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'median'))return this.getStatistics(o,'median');let l=this.quantile(o,0.5);return'string'==typeof o&&this.updateStatistics(o,'median',l),l},Statistics.prototype.mode=function(o){if('undefined'==typeof o)return this.errorMessage('Mode: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'mode'))return this.getStatistics(o,'mode');let l=this.validateInput(o,'nominal','mode');if(!1===l)return;let u=l.data,g=[],h=[u[0]],M=1;for(var S=1;S<l.length;S++){let T=u[S];g[T]=null==g[T]?1:g[T]+1,g[T]>M?(h=[T],M=g[T]):g[T]===M&&h.push(T)}return 1===h.length&&(h=h[0]),'string'==typeof o&&this.updateStatistics(o,'mode',h),h},Statistics.prototype.minimum=function(o){if('undefined'==typeof o)return this.errorMessage('Minimum: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'minimum'))return this.getStatistics(o,'minimum');let l=this.validateInput(o,'ordinal','minimum');if(!1===l)return;let u=Infinity,g=l.length;for(;g--;)l.data[g]<u&&(u=l.data[g]);return'string'==typeof o&&this.updateStatistics(o,'minimum',u),u},Statistics.prototype.maximum=function(o){if('undefined'==typeof o)return this.errorMessage('Maximum: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'maximum'))return this.getStatistics(o,'maximum');let l=this.validateInput(o,'ordinal','maximum');if(!1===l)return;let u=-Infinity,g=l.length;for(;g--;)l.data[g]>u&&(u=l.data[g]);return'string'==typeof o&&this.updateStatistics(o,'maximum',u),u},Statistics.prototype.range=function(o){if('undefined'==typeof o)return this.errorMessage('Range: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'range'))return this.getStatistics(o,'range');let l,u;if('string'==typeof o&&'nominal'===this.getScale(o)){if(l=this.validateInput(o,'nominal','range'),!1===l)return;u=this.getUniqueValues(l.data)}else{if(l=this.validateInput(o,'ordinal','range'),!1===l)return;let g=this.sort(l.data);u=g[l.length-1]-g[0]}return'string'==typeof o&&this.updateStatistics(o,'range',u),u},Statistics.prototype.variance=function(o,l=!0){if('undefined'==typeof o)return this.errorMessage('Variance: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'variance'))return this.getStatistics(o,'variance');let u=this.validateInput(o,'interval','variance');if(!1===u)return;if(2>u.length)return this.errorMessage('The data supplied to compute variance needs to contain at least two datasets.');let g=0;if(this.isNumeric(l)){for(var h=0;h<u.length;h++)g+=_Mathpow(l-u.data[h],2);g/=u.length-1}else{let M=0,S=0;for(var h=0;h<u.length;h++){M+=1;let T=u.data[h]-S;S+=T/M;let C=u.data[h]-S;g+=T*C}l&&1<M?g/=M-1:!l&&0<M?g/=M:g=void 0}return'string'==typeof o&&this.updateStatistics(o,'variance',g),g},Statistics.prototype.standardDeviation=function(o,l=!0){if('undefined'==typeof o)return this.errorMessage('Standard deviation: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'standardDeviation'))return this.getStatistics(o,'standardDeviation');let u=this.validateInput(o,'interval','standard deviation');if(!1!==u){if(2>u.length)return this.errorMessage('The data supplied to compute standardDeviation needs to contain at least two datasets.');let g=_Mathsqrt(this.variance(o,l));return'string'==typeof o&&this.updateStatistics(o,'standardDeviation',g),g}},Statistics.prototype.coefficientOfVariation=function(o,l){if('undefined'==typeof o)return this.errorMessage('Coefficient of variation: No data was supplied.');let u=this.validateInput(o,'interval','coefficient of variation');if(!1!==u){let g=this.standardDeviation(u.data),h='undefined'==typeof l?this.mean(u.data):l;return'undefined'!=typeof g&&'undefined'!=typeof h&&0!==h?g/h:void 0}},Statistics.prototype.indexOfDispersion=function(o,l){if('undefined'==typeof o)return this.errorMessage('Index of dispersion: No data was supplied.');let u=this.validateInput(o,'interval','coefficient of variation');if(!1!==u){let g=this.variance(u.data),h='undefined'==typeof l?this.mean(u.data):l;return'undefined'!=typeof g&&'undefined'!=typeof h&&0!==h?g/h:void 0}},Statistics.prototype.geometricStandardDeviation=function(o){if('undefined'==typeof o)return this.errorMessage('Geomtric standard deviation: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'geometricStandardDeviation'))return this.getStatistics(o,'geometricStandardDeviation');let l=this.validateInput(o,'interval','geometric standard deviation');if(!1===l)return;let u=l.length,g=this.geometricMean(o),h=0,M=!1;for(var S=0;S<u;S++)0>=l.data[S]?M=!0:h+=_Mathpow(_Mathlog(l.data[S]/g),2);return h=M?void 0:_Mathexp(_Mathsqrt(h/u)),'string'==typeof o&&this.updateStatistics(o,'geometricStandardDeviation',h),h},Statistics.prototype.medianAbsoluteDeviation=function(o){if('undefined'==typeof o)return this.errorMessage('Median absolute deviation: No data was supplied.');let l=this.validateInput(o,'interval','median absolute deviation');if(!1===l)return;let u=l.data,g=this.median(u);if('undefined'!=typeof g)return u=u.map((h)=>{return _Mathabs(h-g)}),this.median(u)},Statistics.prototype.cumulativeFrequency=function(o,l){if('undefined'==typeof o)return this.errorMessage('Cumulative frequency: No data was supplied.');if('undefined'==typeof l||!this.isNumeric(l))return void this.errorMessage('You need to specify a boundary for the cumulative frequency analysis that is either an integer or a floating point number.');let u=this.validateInput(o,'ordinal','cumulative frequency analysis');if(!1!==u){let g=this.sort(u.data),h=0;for(;l>=g[h];)h++;return h}},Statistics.prototype.frequencies=function(o){if('undefined'==typeof o)return this.errorMessage('Frequencies: No data was supplied.');let l=this.validateInput(o,'nominal','frequencies');if(!1===l)return;let u=l.data,g={},h=[];for(var M=0;M<l.length;M++){let S=u[M];null==g[S]?(h.push(S),g[S]=1):g[S]++}return h=h.sort((S,T)=>{return g[T]-g[S]}),h=h.map((S)=>{return{value:S,absolute:g[S],relative:g[S]/l.length}}),h},Statistics.prototype.quantile=function(o,l=0.5){if('undefined'==typeof o)return this.errorMessage('Quantile: No data was supplied.');if(!this.isNumeric(l)||0>l||1<l)return this.errorMessage('Quantiles should be called with a percentage value within the range of [0, 1].');let u=this.validateInput(o,'ordinal','quantile');if(!1!==u){let g=l*u.length,h=this.sort(u.data);return 0==g%1?0.5*(h[g]+h[g-1]):h[_Mathfloor(g)]}},Statistics.prototype.quartiles=function(o){if('undefined'==typeof o)return this.errorMessage('Quartiles: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'quartiles'))return this.getStatistics(o,'quartiles');let l=[this.quantile(o,0.25),this.quantile(o,0.75)];return'undefined'!=typeof l[0]&&'undefined'!=typeof l[1]?(this.updateStatistics(o,'quartiles',l),l):void 0},Statistics.prototype.interQuartileRange=function(o){if('undefined'==typeof o)return this.errorMessage('Interquartile range: No data was supplied.');let l=this.validateInput(o,'interval','interquartile range');if(!1!==l){let u=this.quartiles(l.data);return'undefined'==typeof u?void 0:u[1]-u[0]}},Statistics.prototype.skewness=function(o,l=!1){if('undefined'==typeof o)return this.errorMessage('Skewness: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'skewness'))return this.getStatistics(o,'skewness');let u=this.validateInput(o,'ordinal','skewness');if(!1===u)return;if(2>u.length)return;let g=this.mean(o),h=this.standardDeviation(o,!1),M=0;for(var S=0;S<u.length;S++)M+=_Mathpow(u.data[S]-g,3);let T=M/_Mathpow(h,3);return T*=l?u.length/((u.length-1)*(u.length-2)):1/u.length,'string'==typeof o&&this.updateStatistics(o,'skewness',T),T},Statistics.prototype.kurtosis=function(o){if('undefined'==typeof o)return this.errorMessage('Kurtosis: No data was supplied.');if('string'==typeof o&&!1===this.checkLastUpdated(o,'kurtosis'))return this.getStatistics(o,'kurtosis');let l=this.validateInput(o,'ordinal','kurtosis');if(!1===l)return;if(2>l.length)return;let u=this.mean(o),g=this.standardDeviation(o),h=0;for(var M=0;M<l.length;M++)h+=_Mathpow(l.data[M]-u,4);let S=h/(l.length*_Mathpow(g,4));return'string'==typeof o&&this.updateStatistics(o,'kurtosis',S),S},Statistics.prototype.excessKurtosis=function(o){if('undefined'==typeof o)return this.errorMessage('Excess kurtosis: No data was supplied.');let l=this.kurtosis(o);return'undefined'==typeof l?void 0:l-3},Statistics.prototype.sum=function(o){return'undefined'==typeof o?this.errorMessage('Sum: No data given.'):('string'==typeof o&&this.has(this.columns,o)&&(o=this.getColumn(o)),0==o.length?void 0:o.reduce((l,u)=>{return this.isNumeric(u)?l+u:l},0))},Statistics.prototype.sumExact=function(o){if('undefined'==typeof o)return this.errorMessage('Sum exact: No data given.');if('string'==typeof o&&this.has(this.columns,o)&&(o=this.getColumn(o)),0==o.length)return;let l=0,u=0;for(var g=0;g<o.length;g++){let h=this.isNumeric(o[g])?o[g]:0;h-=u;let M=l+h;u=M-l-h,l=M}return l},Statistics.prototype.product=function(o){return'undefined'==typeof o?this.errorMessage('Product: No data given.'):('string'==typeof o&&this.has(this.columns,o)&&(o=this.getColumn(o)),0===o.length?1:o.reduce((l,u)=>{return this.isNumeric(u)?l*u:l},1))},Statistics.prototype.factorial=function(o){return this.isNumeric(o)&&!_NumberisInteger(o)?this.gamma(o):'undefined'==typeof this.factorials[o]?this.computeFactorial(o):this.factorials[o]},Statistics.prototype.computeFactorial=function(o){if('undefined'==typeof o||!this.isNumeric(o)||0>o)return;if('undefined'!=typeof this.factorials[o])return this.factorials[o];if(!_NumberisInteger(o))return this.gamma(o);let l=1,u=1;for(;o>u;)u++,l*=u,'undefined'==typeof this.factorials[u]&&(this.factorials[u]=l);return l},Statistics.prototype.binomialCoefficient=function(o=1,l=1){if(o<l||0>l)return this.errorMessage('The binomial coefficient is only defined for n and k with n \u2265 k \u2265 0. N is '+o+' and k is '+l+'.');if(!_NumberisInteger(o)||!_NumberisInteger(l))return this.errorMessage('The binomial coefficient is only defined for integers n and k.');let u=[];for(var g=1;g<=l;g++)u.push((o+1-g)/g);return this.product(u)},Statistics.prototype.gamma=function(o,l=!1){return'undefined'==typeof o||!this.isNumeric(o)||0>o?void 0:_NumberisInteger(o)&&'undefined'!=typeof this.factorials[o-1]?this.factorials[o-1]:l?this.gammaSpouge(o):this.gammaStirling(o)},Statistics.prototype.gammaSpouge=function(o){if('undefined'==typeof o||!this.isNumeric(o)||0>o)return;if(_NumberisInteger(o)&&'undefined'!=typeof this.factorials[o-1])return this.factorials[o-1];const l=this.spougeConstant;let u=_Mathpow(o+l,o+0.5),g=1,h=0,M=_Mathsqrt(2*_MathPI);u*=_Mathexp(-o-l),u/=o;for(var S=1;S<l;S++)o++,h=_Mathpow(l-S,S-0.5),h*=_Mathexp(l-S),h/=g,M+=h/o,g*=-S;return M*u},Statistics.prototype.gammaStirling=function(o){if('undefined'==typeof o||!this.isNumeric(o)||0>o)return;if(_NumberisInteger(o)&&'undefined'!=typeof this.factorials[o-1])return this.factorials[o-1];let g=1/(10*o);return g=1/(12*o-g),g=(g+o)*0.36787944117144233,g=_Mathpow(g,o),g*=_Mathsqrt(6.283185307179586/o),g},Statistics.prototype.incompleteGamma=function(o,l){if('undefined'==typeof l)return this.errorMessage('The incomplete lower gamma function is only defined for two numeric variables s and x.');if(!this.isNumeric(o)||!this.isNumeric(l))return this.errorMessage('The incomplete lower gamma function is only defined for numeric variables s and x.');if(0>l)return this.errorMessage('The incomplete lower gamma function is defined for x > 0.');let u=this.incompleteGammaIterations,g=1;for(var h=0;h<u;h++){let M=u-h;g=l+(M-o)/(1+M/g)}return this.gamma(o,!0)-_Mathexp(-l)*_Mathpow(l,o)/g},Statistics.prototype.regularisedGamma=function(o,l){return'undefined'==typeof l?this.errorMessage('The regularised lower gamma function is only defined for two numeric variables s and x.'):this.isNumeric(o)&&this.isNumeric(l)?0>l?this.errorMessage('The regularised lower gamma function is defined for x > 0.'):this.incompleteGamma(o,l)/this.gamma(o,!0):this.errorMessage('The regularised lower gamma function is only defined for numeric variables s and x.')},Statistics.prototype.beta=function(o,l){return'undefined'==typeof l?this.errorMessage('The beta function is only defined for two numeric variables a and b.'):this.isNumeric(o)&&this.isNumeric(l)?0>=o||0>=l?this.errorMessage('The beta function is defined for a and b with a > 0 and b > 0.'):_NumberisInteger(o)&&_NumberisInteger(l)&&0<o&&0<l?this.factorial(o-1)*this.factorial(l-1)/this.factorial(o+l-1):this.gamma(o,!0)*this.gamma(l,!0)/this.gamma(o+l,!0):this.errorMessage('The beta function is only defined for numeric variables a and b.')},Statistics.prototype.incompleteBeta=function(o,l,u){if('undefined'==typeof u)return this.errorMessage('The incomplete beta function is only defined for two numeric variables a and b.');if(!this.isNumeric(o)||!this.isNumeric(l)||!this.isNumeric(u))return this.errorMessage('The incomplete beta function is only defined for numeric variables x, a and b.');if(0>o||1<o)return this.errorMessage('The incomplete beta function is defined for x \u2265 0 and x \u2266 1.');if(0>=l||0>=u)return this.errorMessage('The incomplete beta function is defined for a and b with a > 0 and b > 0.');if(1==o)return this.beta(l,u);var g=function(N,I,V,D){if(0==N%2){let F=0.5*N;return F*(V-F)*D/((I+2*F-1)*(I+2*F))}let F=0.5*N-0.5;return-(I+F)*(I+V+F)*D/((I+2*F)*(I+2*F+1))};let h=_Mathpow(o,l)*_Mathpow(1-o,u)/l,M=this.incompleteBetaIterations,S=1;for(var T=0;T<M;T++){let N=M-T;S=1+g(N,l,u,o)/S}let C=h/S;return C},Statistics.prototype.regularisedBeta=function(o,l,u){if('undefined'==typeof u)return this.errorMessage('The regularised beta function is only defined for two numeric variables a and b.');if(!this.isNumeric(o)||!this.isNumeric(l)||!this.isNumeric(u))return this.errorMessage('The regularised beta function is only defined for numeric variables x, a and b.');if(1<o||0>o)return this.errorMessage('The regularised beta function is defined for x \u2265 0 and x \u2266 1.');if(0>=l||0>=u)return this.errorMessage('The regularised beta function is defined for a and b with a > 0 and b > 0.');if(!_NumberisInteger(l)||!_NumberisInteger(u))return this.incompleteBeta(o,l,u)/this.beta(l,u);let g=this.epsilon+1,h=l,M=0;for(;g>=this.epsilon;)g=this.binomialCoefficient(u+h-1,h)*_Mathpow(o,h),M+=g,h++;return M*_Mathpow(1-o,u)},Statistics.prototype.covariance=function(o,l,u=!0){if('undefined'==typeof l)return this.errorMessage('Covariance requires two variables to be compared.');let g=this.validateInput(o,'interval','covariance');if(!1===g)return;let h=this.validateInput(l,'interval','covariance');if(!1===h)return;let M=this.reduceToPairs(g.data,h.data);if(0===M.length)return;let S=this.mean(M.valuesFirst),T=this.mean(M.valuesSecond),C=0;for(var N=0;N<M.length;N++)C+=(M.valuesFirst[N]-S)*(M.valuesSecond[N]-T);return u&&1<M.length?C/=M.length-1:!u&&0<M.length?C/=M.length:C=void 0,{covariance:C,missings:M.missings}},Statistics.prototype.correlationCoefficient=function(o,l){if('undefined'==typeof l)return this.errorMessage('Pearson correlation coefficient requires two variables to be compared.');let u=this.validateInput(o,'interval','Pearson correlation coefficient');if(!1===u)return;let g=this.validateInput(l,'interval','Pearson correlation coefficient');if(!1===g)return;let h=u.length>=g.length?u.length:g.length,M=u.data,S=g.data,T=[],C=0,N=0;for(var I=0;I<h;I++){let U=M[I],O=S[I];void 0===typeof U||void 0===typeof O||isNaN(U)||isNaN(O)||(C+=U,N+=O,T.push([U,O]))}let V=h-T.length;if(h=T.length,0===h)return;C/=h,N/=h;let D=0,F=0,P=0;for(var I=0;I<h;I++){let U=T[I][0]-C,O=T[I][1]-N;D+=U*O,F+=U*U,P+=O*O}let B=0<F&&0<P?D/_Mathsqrt(F*P):0;return{correlationCoefficient:B,missings:V}},Statistics.prototype.spearmansRho=function(o,l,u=!1){if('undefined'==typeof l)return this.errorMessage('Spearman\'s Rho requires two variables to be compared.');let g=this.validateInput(o,'ordinal','Spearman\'s Rho');if(!1===g)return;let h=this.validateInput(l,'ordinal','Spearman\'s Rho');if(!1===h)return;let M=this.reduceToPairs(o,l),S=M.length;if(0===S)return;let T=this.assignRanks(o,{data:M.valuesCombined,returnFrequencies:!0,order:'desc'}),C=T.frequencies;T=this.assignRanks(l,{data:T.data,returnFrequencies:!0,order:'desc'});let N=T.frequencies;T=T.data;let I=T.reduce((O,R)=>{return O+_Mathpow(R['rank-'+o]-R['rank-'+l],2)},0),V=6*I;if(u){let O=Object.values(C).reduce((L,E)=>{return L+_Mathpow(E,3)-E}),R=Object.values(N).reduce((L,E)=>{return L+_Mathpow(E,3)-E}),G=_Mathpow(S,3)-S-0.5*O-0.5*R-V,A=_Mathsqrt((_Mathpow(S,3)-S-O)*(_Mathpow(S,3)-S-R));V=G/A}else V=1-V/(_Mathpow(S,3)-S);let D=S-2,F=_Mathsqrt((D-1)/1.06)*this.fisherTransformation(V),P=1-this.normalCumulativeValue(_Mathabs(F)),B=V*_Mathsqrt(D/(1-V*V)),U=1-this.studentsTCumulativeValue(_Mathabs(B),D);return{rho:V,significanceNormal:{zScore:F,pOneTailed:P,pTwoTailed:2*P},significanceStudent:{degreesOfFreedom:D,tStatistic:B,pOneTailed:U,pTwoTailed:2*U},missings:M.missings}},Statistics.prototype.kendallsTau=function(o,l){if('undefined'==typeof l)return this.errorMessage('Kendall\'s Tau requires two columns to analyze.');let u=this.validateInput(o,'ordinal','Kendall\'s Tau');if(!1===u)return;let g=this.validateInput(l,'ordinal','Kendall\'s Tau');if(!1===g)return;let h=this.reduceToPairs(o,l),M=h.length,S=h.valuesCombined,T=0,C=0,N={},I={},V=0;for(var D=0;D<M-1;D++)for(var F=D+1;F<M;F++){let X=S[D][o],Q=S[F][o],H=S[D][l],J=S[F][l];X===Q?H===J?V+=1:N[H]=this.has(N,H)?N[H]+1:1:H===J?I[H]=this.has(I,H)?I[H]+1:1:_Mathsign(X-Q)===_Mathsign(H-J)?T+=1:C+=1}let P=T-C,B=0===Object.keys(N).length+Object.keys(I).length?2*P/(M*(M-1)):void 0,U=3*P/_Mathsqrt(0.5*M*(M-1)*(2*M+5)),O=this.normalCumulativeValue(-_Mathabs(U)),R=2<h.length?2:h.length,A=B,L=U,E=O;if('undefined'==typeof B){A=P/_Mathsqrt((T+C+Object.keys(N).length)*(T+C+Object.keys(I).length));let X=0,Q=0,H=0,J=0,$=0;for(var W in N)X+=W*(W-1)*(2*W+5),H+=W*(W-1),J+=W*(W-1)*(W-2);for(var W in I)Q+=W*(W-1)*(2*W+5),J+=W*(W-1)/(2*M*(M-1)),$+=W*(W-1)*(W-2)/(9*M*(M-1)*(M-2));L=M*(M-1)*(2*M+5),L=(L-X-Q)/18+H*J+0*$,L=P/_Mathsqrt(L),E=this.normalCumulativeValue(-_Mathabs(L))}let K='undefined'==typeof B?void 0:{tauA:B,z:U,pOneTailed:O,pTwoTailed:2*O},Y='undefined'==typeof B?{tauB:A,z:L,pOneTailed:E,pTwoTailed:2*E}:{tauB:B,z:U,pOneTailed:O,pTwoTailed:2*O};return{a:K,b:Y,c:{tauC:2*R*P/(M*M*(R-1))},missings:h.missings}},Statistics.prototype.goodmanKruskalsGamma=function(o,l){if('undefined'==typeof l)return this.errorMessage('Goodman and Kruskal\'s Gamma requires two columns to analyze.');let u=this.validateInput(o,'ordinal','Goodman and Kruskal\'s Gamma');if(!1===u)return;let g=this.validateInput(l,'ordinal','Goodman and Kruskal\'s Gamma');if(!1===g)return;let h=this.reduceToPairs(o,l),M=h.valuesCombined,S=h.length,T=0,C=0;for(var N=0;N<S-1;N++)for(var I=N+1;I<S;I++){let P=M[N][o],B=M[I][o],U=M[N][l],O=M[I][l];P===B||U===O||(_Mathsign(P-B)===_Mathsign(U-O)?T+=1:C+=1)}let V=(T-C)/(T+C),D=V*_Mathsqrt((T+C)/(S*(1-V*V))),F=1-this.studentsTCumulativeValue(_Mathabs(D),S-2);return{gamma:V,tStatistic:D,pOneTailed:F,pTwoTailed:2*F,missings:h.missings}},Statistics.prototype.fisherTransformation=function(o){return'undefined'==typeof o||!this.isNumeric(o)||-1>o||1<o?this.errorMessage('Fisher transformation is only defined for a Pearson correlation coefficient within the interval of [-1, 1].'):Math.atanh(o)||0.5*_Mathlog((1+o)/(1-o))},Statistics.prototype.linearRegression=function(o,l){if('undefined'==typeof l)return this.errorMessage('Linear regression requires two columns to compare.');let u=this.validateInput(o,'interval','linear regression');if(!1===u)return;let g=this.validateInput(l,'interval','linear regression');if(!1===g)return;let h=this.reduceToPairs(u.data,g.data),M=h.valuesFirst,S=h.valuesSecond,T=h.missings,C=h.length;if(0===C)return;let N=this.mean(M),I=this.mean(S),V=0,D=0,F=0;for(var P=0;P<C;P++){let W=M[P]-N,K=S[P]-I;F+=W*K,V+=W*W,D+=K*K}if(0==V||0==D)return;let B=F/V,U=F/D,G=F/_Mathsqrt(V*D),A=G*G,L=2<C?1-(1-A)*(C-1)/(C-2):void 0,E=180*Math.acos(G)/_MathPI;return 90<E&&(E=180-E),{regressionFirst:{beta1:I-B*N,beta2:B},regressionSecond:{beta1:N-U*I,beta2:U},coefficientOfDetermination:A,coefficientOfDeterminationCorrected:L,correlationCoefficient:G,phi:E}},Statistics.prototype.normalProbabilityDensity=function(o,l=0,u=1){if('undefined'==typeof o)return this.errorMessage('Normal probability density: no x is given.');if(0>=u)return this.errorMessage('Normal probability density: variance must be larger than 0.');let g=-_Mathpow(o-l,2)/(2*u);return _Mathexp(g)/_Mathsqrt(2*_MathPI*u)},Statistics.prototype.normalDistribution=function(o=0,l=1){if(0>=l)return this.errorMessage('Normal distribution: variance must be larger than 0.');let u=0,g=1,h={};for(;g>=this.epsilon&&(g=this.normalProbabilityDensity(o+u,o,l),!(g<this.epsilon));)h[(o+u).toFixed(2)]=g,h[(o-u).toFixed(2)]=g,u+=0.01;return h},Statistics.prototype.normalCumulativeValue=function(o){if('undefined'==typeof o)return this.errorMessage('Normal cumulative value: no z is given.');let l=o,u=o;for(var g=1;g<this.zTableIterations;g++)u*=o*o/(2*g+1),l+=u;return _Mathround(1e5*(0.5+l/_Mathsqrt(2*_MathPI)*_Mathexp(-0.5*o*o)))/1e5},Statistics.prototype.normalCumulativeDistribution=function(){let o=this.zTable;if('undefined'==typeof o){o={};for(var l=0;4.09>=l;l+=0.01){let u=_Mathround(100*l)/100;o[u.toFixed(2)]=this.normalCumulativeValue(l)}this.zTable=o}return o},Statistics.prototype.binomialProbabilityMass=function(o,l=10,u=0.5){return'undefined'==typeof o?this.errorMessage('Binomial probability mass: the required argument k was not given.'):0>o||!_NumberisInteger(o)?this.errorMessage('Binomial probability mass: k must be a non-negative integer.'):0>l||!_NumberisInteger(l)?this.errorMessage('Binomial probability mass: n must be a non-negative integer.'):0>u||1<u?this.errorMessage('Binomial probability mass: The probability must lie within the range of [0, 1].'):this.binomialCoefficient(l,o)*_Mathpow(u,o)*_Mathpow(1-u,l-o)},Statistics.prototype.binomialDistribution=function(o=10,l=0.5){if(0>o||!_NumberisInteger(o))return this.errorMessage('Binomial distribution: n must be a non-negative integer.');if(0>l||1<l)return this.errorMessage('Binomial distribution: The probability must lie within the range of [0, 1].');let u=0,g=0,h=0,M=[],S=1;for(;u<=o;)g=S*_Mathpow(l,u)*_Mathpow(1-l,o-u),M.push(g),h+=g,u++,S=S*(o+1-u)/u;return M},Statistics.prototype.binomialCumulativeValue=function(o,l=10,u=0.5){return'undefined'==typeof o?this.errorMessage('Binomial cumulative distribution value: the required argument k was not given.'):0>o||!_NumberisInteger(o)?this.errorMessage('Binomial cumulative distribution value: k must be a non-negative integer.'):0>l||!_NumberisInteger(l)?this.errorMessage('Binomial cumulative distribution value: n must be a non-negative integer.'):0>u||1<u?this.errorMessage('Binomial cumulative distribution value: The probability must lie within the range of [0, 1].'):this.regularisedBeta(1-u,l-o,o+1)},Statistics.prototype.binomialCumulativeDistribution=function(o=10,l=0.5){if(0>o||!_NumberisInteger(o))return this.errorMessage('Binomial cumulative distribution: n must be a non-negative integer.');if(0>l||1<l)return this.errorMessage('Binomial cumulative distribution: The probability must lie within the range of [0, 1].');let u=this.binomialDistribution(o,l),g=0;return u.map(function(h){return g=this.sumExact([g,h]),g},this)},Statistics.prototype.poissonProbabilityMass=function(o,l=1){if('undefined'==typeof o||!_NumberisInteger(o))return this.errorMessage('Poisson probability mass: the required argument k must be an integer.');if(0>o||0>=l)return this.errorMessage('Poisson probability mass: Both k and lambda must be larger than 0.');if(10<o){let g=1;for(var u=1;u<=o;u++)g*=l*_Mathexp(-l/o)/u;return g}return _Mathexp(-l)*_Mathpow(l,o)/this.factorial(o)},Statistics.prototype.poissonDistribution=function(o=1){if(0>=o)return this.errorMessage('Poisson distribution: Lambda must be larger than 0.');let l=0,u=0,g=[];for(;u<1-this.epsilon;){let h=this.poissonProbabilityMass(l,o);g.push(h),u+=h,l++}return g},Statistics.prototype.poissonCumulativeValue=function(o,l=1){if('undefined'==typeof o||!_NumberisInteger(o))return this.errorMessage('Poisson cumulative distribution: The number of cumulative events k must be supplied.');if(0>o||0>=l)return this.errorMessage('Poisson distribution: Both k and lambda must be larger than 0.');let u=this.poissonDistribution(l);return o<u.length-1?this.sumExact(u.slice(0,o+1)):1},Statistics.prototype.poissonCumulativeDistribution=function(o=1){if(0>=o)return this.errorMessage('Poisson distribution: lambda must be larger than 0.');let l=this.poissonDistribution(o),u=0;return l.map(function(g){return u=this.sumExact([u,g]),u},this)},Statistics.prototype.studentsTProbabilityDensity=function(o,l){if('undefined'==typeof l)return this.errorMessage('Student\'s t-distribution probability density: no value for degrees of freedom (df) given.');if(0>=l)return this.errorMessage('Student\'s t-distribution probability density: degrees of freedom (df) must be larger than 0.');let u=_Mathpow(1+o*o/l,-0.5*(l+1));return u/=_Mathsqrt(l)*this.beta(0.5,0.5*l),u},Statistics.prototype.studentsTDistribution=function(o){if('undefined'==typeof o)return this.errorMessage('Student\'s t-distribution: no value for degrees of freedom (df) given.');if(0>=o)return this.errorMessage('Student\'s t-distribution: degrees of freedom (df) must be larger than 0.');let l=0,u=1,g={};for(;u>=this.epsilon&&(u=this.studentsTProbabilityDensity(l,o),!(u<this.epsilon));)g[l.toFixed(2)]=u,g[(-l).toFixed(2)]=u,l+=0.01;return g},Statistics.prototype.studentsTCumulativeValue=function(o,l){return'undefined'==typeof l?this.errorMessage('Student\'s cumulative t-distribution value: no value for degrees of freedom (df) given.'):0>=l?this.errorMessage('Student\'s cumulative t-distribution value: degrees of freedom (df) must be larger than 0.'):0>=o?0.5*this.regularisedBeta(l/(o*o+l),0.5*l,0.5):0.5+0.5*this.regularisedBeta(o*o/(o*o+l),0.5,0.5*l)},Statistics.prototype.studentsTCumulativeDistribution=function(o){if('undefined'==typeof o)return this.errorMessage('Student\'s cumulative t-distribution: no value for degrees of freedom (df) given.');if(0>=o)return this.errorMessage('Student\'s cumulative t-distribution: degrees of freedom (df) must be larger than 0.');let l=0,u=0,g=-0.1,h={};for(;u<=1-this.epsilon&&(u=this.studentsTCumulativeValue(l,o),!(g>=u));)h[l.toFixed(2)]=u,h[(-l).toFixed(2)]=u,g=u,l+=0.01;return h},Statistics.prototype.chiSquaredProbabilityDensity=function(o,l){return'undefined'==typeof l?this.errorMessage('Chi squared distribution probability density: no value for degrees of freedom (df) given.'):0>=l?this.errorMessage('Chi squared distribution probability density: degrees of freedom (df) must be larger than 0.'):0>=o?0:_Mathpow(o,0.5*l-1)*_Mathexp(-0.5*o)/(_Mathpow(2,0.5*l)*this.gamma(0.5*l,!0))},Statistics.prototype.chiSquaredDistribution=function(o){if('undefined'==typeof o)return this.errorMessage('Chi squared distribution: no value for degrees of freedom (df) given.');if(0>=o)return this.errorMessage('Chi squared distribution: degrees of freedom (df) must be larger than 0.');let l=0.01,u=1,g={'0.00':0};for(;(2>=o&&u>=this.epsilon||2<o&&l<=o-2||2<o&&u>=this.epsilon)&&(u=this.chiSquaredProbabilityDensity(l,o),!(u<this.epsilon&&l>=o-2&&2<o));)g[l.toFixed(2)]=u,l+=0.01;return g},Statistics.prototype.chiSquaredCumulativeValue=function(o,l){return'undefined'==typeof l?this.errorMessage('Chi squared cumulative distribution value: no value for degrees of freedom (df) given.'):0>=l?this.errorMessage('Chi squared cumulative distribution value: degrees of freedom (df) must be larger than 0.'):0>=o?0:this.regularisedGamma(0.5*l,0.5*o)},Statistics.prototype.chiSquaredCumulativeDistribution=function(o){if('undefined'==typeof o)return this.errorMessage('Chi squared cumulative distribution: no value for degrees of freedom (df) given.');if(0>=o)return this.errorMessage('Chi squared cumulative distribution: degrees of freedom (df) must be larger than 0.');let l=0.01,u=0,g={'0.00':0};for(;u<=1-this.epsilon&&(u=this.chiSquaredCumulativeValue(l,o),!(u>=1-this.epsilon));)0<u&&(g[l.toFixed(2)]=u),l+=0.01;return g},Statistics.prototype.barnardsTest=function(o,l){if('undefined'==typeof l)return this.errorMessage('Barnard\'s test: No data was supplied.');let u=this.contingencyTable(o,l,'Barnard\'s test');if('undefined'==typeof u)return;let{a:g,b:h,c:M,d:S}=u,T=g+h+M+S;if(T>this.maxBarnardsN)return this.errorMessage('Barnard\'s test is a resource-intensive method, relative to the total number of datasets to analyze. There are '+T+' datasets in the supplied data, exceeding the maxinum of '+this.maxBarnardsN+'. You can change this number by changing the "maxBarnardsN" option (be cautious).');var C=(g+h)/T;C=C*(1-C)*(1/(g+M)+1/(h+S)),C=(h/(h+S)-g/(g+M))/_Mathsqrt(C),isNaN(C)&&(C=0);let N=[];for(var I=0;1>I;I=this.sumExact([I,1e-3])){let F=0;for(var V=0;V<=g+M;V++)for(var D=0;D<=h+S;D++){let P=(V+D)/T;if(P=P*(1-P)*(1/(g+M)+1/(h+S)),P=(V/(g+M)-D/(h+S))/_Mathsqrt(P),!isNaN(P)&&_Mathabs(P)>=_Mathabs(C)){let B=this.binomialCoefficient(g+M,V)*this.binomialCoefficient(h+S,D);B*=_Mathpow(I,V+D)*_Mathpow(1-I,T-V-D),F+=isNaN(B)?0:B}}N.push({nuisance:I,significance:F})}return N=this.sortDataByColumn('significance',{data:N,order:'desc'}),{wald:C,nuisance:N[0].nuisance,pOneTailed:0.5*N[0].significance,pTwoTailed:N[0].significance}},Statistics.prototype.binomialTest=function(o,l,u=0.5){if('undefined'==typeof l)return this.errorMessage('Binomial test requires the data to test and a value which is hypotethised to be observed with a probability of alpha.');if(0>u||1<u)return this.errorMessage('Binomial test is only defined for probabilities alpha with alpha \u2265 0 and alpha \u2266 1.');let g=this.getScale(o);if('interval'===g||'metric'===g)return this.errorMessage('Binomial test is only defined for data of nominal or ordinal dichotomic scale.');let h=this.validateInput(o,'nominal','binomial test');if(!1!==h){let M=this.getUniqueValues(h.data);if(2<M.length)return this.errorMessage('Binomial test is only defined for dichotomic data. The supplied data has '+M.length+' unique values.');if(2===M.length&&0>M.indexOf(l))return this.errorMessage('The value "'+l+'" was not found in the supplied data.');let S=h.data.filter(function(I){return I===l}).length,T=this.binomialProbabilityMass(S,h.length,u),C=this.binomialCumulativeValue(S-1,h.length,u),N=1-C-T;return{pExactly:T,pFewer:C,pAtMost:C+T,pMore:N,pAtLeast:N+T}}},Statistics.prototype.signTest=function(o,l){if('undefined'==typeof l)return this.errorMessage('Sign test: No data was supplied.');let u=this.validateInput(o,'ordinal','sign test'),g=this.validateInput(l,'ordinal','sign test');if(!1===u||!1===g)return;if(0===u.length||0===g.length)return;let h=this.reduceToPairs(u.data,g.data),M=h.missings,S=h.length,T=h.valuesFirst,C=h.valuesSecond,N=0;for(var I=0;I<S;I++)T[I]>C[I]&&(N+=1);let V=this.binomialProbabilityMass(N,S),D=this.binomialCumulativeValue(N-1,S),F=1-D-V;return{positives:N,pExactly:V,pFewer:D,pAtMost:D+V,pMore:F,pAtLeast:F+V}},Statistics.prototype.fishersExactTest=function(o,l){if('undefined'==typeof l)return this.errorMessage('Fisher\'s exact test requires two columns to analyze.');let u=this.contingencyTable(o,l,'Fisher\'s exact test');if('undefined'!=typeof u){let{a:g,b:h,c:M,d:S}=u,T=this.binomialCoefficient(g+h,g)*this.binomialCoefficient(M+S,M)/this.binomialCoefficient(g+h+M+S,g+M);return T}},Statistics.prototype.mannWhitneyU=function(o,l){if('undefined'==typeof l)return this.errorMessage('Mann-Whitney-U test requires two columns to analyze.');let u=this.validateInput(o,'nominal','Mann-Whitney-U test'),g=this.validateInput(l,'ordinal','Mann-Whitney-U test');if(!1===u||!1===g)return;if(0===u.length||0===g.length)return;let h=this.sort(g.data),M=this.getUniqueValues(u.data);if(2!==M.length)return this.errorMessage('The Mann-Whitney-U test requires the independent variable to have exactly two unique values. Variable "'+independentValue+'" has '+M.length+' different values: '+u.data.join(', '));let S=this.assignRanks(l),T=S.reduce((O,R)=>{return R[o]===M[0]?O+R['rank-'+l]:O},0),C=S.reduce((O,R)=>{return R[o]===M[0]?O+1:O},0),N=S.reduce((O,R)=>{return R[o]===M[1]?O+R['rank-'+l]:O},0),I=S.reduce((O,R)=>{return R[o]===M[1]?O+1:O},0),F=Math.min(C*(0.5*C+I+0.5)-T,I*(0.5*I+C+0.5)-N),P=(F-0.5*C*I)/_Mathsqrt(C*I*(C+I+1)/12),B=1-this.normalCumulativeValue(_Mathabs(P));return{MannWhitneyU:F,zScore:P,pOneTailed:B,pTwoTailed:2*B}},Statistics.prototype.chiSquaredTest=function(o,l){if('undefined'==typeof l)return this.errorMessage('Chi Squared Test: You need to specify two variables, either of nominal or ordinal scale.');let u=this.getScale(o),g=this.getScale(l);if('ordinal'!==u&&'nominal'!==u||'ordinal'!==g&&'nominal'!==g)return this.errorMessage('Chi Squared Test: Both variables need to be either of nominal or ordinal scale.');let h=this.contingencyTable(o,l);if('undefined'==typeof h)return this.errorMessage('Chi Squared Test: Failed to create a contingency table. Please make sure your data is prepared correctly.');h=h.detailled;let M=h.total.total,S=0,T=Object.keys(h).length-1;for(var C in T=(T-1)*(Object.keys(h.total).length-T-2),h)if(this.has(h,C)&&'total'!=C){let V=h[C].total;for(var N in h[C])if(this.has(h[C],N)&&'total'!=N){let D=h.total[N],F=V*D/M;S+=_Mathpow(h[C][N]-F,2)/F}}let I;return I=0>S||1>T?0:1-this.chiSquaredCumulativeValue(S,T),{PearsonChiSquared:S,degreesOfFreedom:T,significance:I}},Statistics.prototype.studentsTTestOneSample=function(o,l){if('undefined'==typeof l||!this.isNumeric(l))return this.errorMessage('Student\'s t-test (one sample) requires data and the mean for which the null hypothesis should hold true.');let u=this.validateInput(o,'interval','student\'s t-test (one sample)');if(!1===u)return;if(0===u.length)return;let g=this.mean(u.data),h=this.standardDeviation(u.data),M=_Mathsqrt(u.length)*(g-l)/h,S=u.length-1,T=this.studentsTCumulativeValue(_Mathabs(M),S);return 0.5<T&&(T=1-T),{tStatistic:M,degreesOfFreedom:S,pOneSided:T,pTwoSided:2*T}},Statistics.prototype.studentsTTestTwoSamples=function(o,l,{nullHypothesisDifference:u=0,dependent:g=!1}={}){if('undefined'==typeof l)return this.errorMessage('Student\'s t-test (two sample) requires data for two columns and the difference of their means for which the null hypothesis should hold true.');let h=this.validateInput(o,'interval','student\'s t-test (two sample)'),M=this.validateInput(l,'interval','student\'s t-test (two sample)');if(!1===h||!1===M)return;let N,I,S=h.length,T=M.length,C={};if(0===S||0===T)return;if(g){let F=this.reduceToPairs(h.data,M.data),P=F.valuesFirst,B=F.valuesSecond,U=0,O=0;for(var V=0;V<F.length;V++)O+=P[V]-B[V];O/=F.length;for(var V=0;V<F.length;V++)U+=_Mathpow(P[V]-B[V]-O,2);U=_Mathsqrt(U/(F.length-1)),N=_Mathsqrt(S)*(O-u)/U,I=F.length-1,C={tStatistic:N,degreesOfFreedom:I,missings:F.missings}}else{let F=this.mean(h.data),P=this.mean(M.data),B=this.variance(h.data),U=this.variance(M.data),O=_Mathsqrt(((S-1)*B+(T-1)*U)/(S+T-2));N=(F-P-u)/O,N*=_Mathsqrt(S*T/(S+T)),I=S+T-2,C={tStatistic:N,degreesOfFreedom:I}}let D=this.studentsTCumulativeValue(N,I);return 0.5<D&&(D=1-D),C.pOneSided=D,C.pTwoSided=2*D,C},Statistics.prototype.gaussianError=function(o){if('undefined'==typeof o||!this.isNumeric(o))return this.errorMessage('Gaussian Error Function: No valid value for x supplied. X needs to be numeric.');let l=1/(1+0.5*_Mathabs(o)),u=-o*o-1.26551223+1.00002368*l+0.37409196*l*l+0.09678418*_Mathpow(l,3)-0.18628806*_Mathpow(l,4)+0.27886807*_Mathpow(l,5)-1.13520398*_Mathpow(l,6)+1.48851587*_Mathpow(l,7)-0.82215223*_Mathpow(l,8)+0.17087277*_Mathpow(l,9);return u=_Mathexp(u)*l,0<=o?1-u:u-1},Statistics.prototype.inverseGaussianError=function(o){if('undefined'==typeof o||!this.isNumeric(o))return this.errorMessage('Inverse Gaussian Error Function: No valid value for x supplied. X needs to be numeric.');if(1<o)return this.errorMessage('Inverse Gaussian Error Function: x can not be larger than 1.');if(-1>o)return this.errorMessage('Inverse Gaussian Error Function: x can not be smaller than -1.');var u,l=-_Mathlog((1-o)*(1+o));return 5>l?(l-=2.5,u=+3.43273939e-7+ +2.81022636e-8*l,u=+-3.5233877E-6+u*l,u=+-4.39150654E-6+u*l,u=2.1858087e-4+u*l,u=-0.00125372503+u*l,u=-0.00417768164+u*l,u=0.246640727+u*l,u=1.50140941+u*l):(l=_Mathsqrt(l)-3,u=1.00950558e-4-2.00214257e-4*l,u=0.00134934322+u*l,u=-0.00367342844+u*l,u=0.00573950773+u*l,u=-0.0076224613+u*l,u=0.00943887047+u*l,u=1.00167406+u*l,u=2.83297682+u*l),(u*o).toFixed(7)},Statistics.prototype.probit=function(o){return'undefined'!=typeof o&&this.isNumeric(o)?0>o||1<o?this.errorMessage('Probit is only defined for quantiles p with 1 \u2265 p \u2265 0.'):0===o?-Infinity:1===o?Infinity:1.4142135623730951*this.inverseGaussianError(2*o-1):this.errorMessage('Probit: No valid value for quantile supplied. quantile needs to be numeric.')},Statistics.prototype.fisherYatesShuffle=function(o,l=Math.random){if('undefined'==typeof o)return this.errorMessage('Fisher-Yates shuffle: No data given.');let u=this.validateInput(o,'nominal','');if(!1===u)return;let M,S,g=u.data,h=u.length;for(;h;)S=_Mathfloor(l()*h--),M=g[h],g[h]=g[S],g[S]=M;return g},Statistics.prototype.xorshift=function(o,l=0){if('undefined'==typeof o||o.constructor!==Array||4!==o.length)return this.errorMessage('Xorshift needs to be seeded with an array consisting of four numbers.');if(!_NumberisInteger(l)||0>l)return this.errorMessage('Xorshift: startIndex must be a non-negative integer.');const u=4,g=64;let h=0,M=u,S=new Uint32Array(g);S[0]=o[0],S[1]=o[1],S[2]=o[2],S[3]=o[3];const T=function(I,V,D){for(var F=V;F<D;F++){let P=(I[0]^I[0]<<11)>>>0;I[0]=I[1],I[1]=I[2],I[2]=I[3],I[3]=((I[3]^I[3]>>>19)>>>0^(P^P>>>8)>>>0)>>>0,I[F]=I[3]}return I};this.next=function(I=!0){let V=S[M];return h+=1,M++>=g&&(M=u,T(S,u,g)),I?V/4294967296:V},S=T(S,u,g);for(var C=0;C<l;C++)this.next()},Statistics.prototype.boxMuller=function(o=0,l=1,{randomSourceA:u=Math.random,randomSourceB:g=Math.random}={}){let h=0,M=0,S=0,T=0;do h=u(),S+=1;while((0>=h||1<=h)&&50>S);do M=g(),T+=1;while((0>=M||1<=M)&&50>T);for(;0>=h||1<=h;)h=Math.random();for(;0>=M||1<=M;)M=Math.random();let C=_Mathsqrt(-2*_Mathlog(h))*Math.cos(2*_MathPI*M);return C*l+o},Statistics.prototype.ziggurat=function(o=0,l=1){let u=123456789,g=[128],h=[128],M=[128];const S=function(I,V){let P,B,D=3.442619855899,F=1/D;for(;;){if(P=I*g[V],0===V){for(P=-_Mathlog(C())*F,B=-_Mathlog(C());B+B<P*P;)P=-_Mathlog(C())*F,B=-_Mathlog(C());return 0<I?D+P:-D-P}if(h[V]+C()*(h[V-1]-h[V])<_Mathexp(-0.5*P*P))return P;if(I=T(),V=127&I,_Mathabs(I)<M[V])return I*g[V]}},T=function(){let I=u,V=u;return V^=V<<13,V^=V>>>17,V^=V<<5,u=V,0|I+V},C=function(){return 0.5*(1+T()/-2147483648)};(function(){u^=new Date().getTime();let I=2147483648,V=3.442619855899,D=V,F=0.00991256303526217,P=F/_Mathexp(-0.5*V*V);M[0]=_Mathfloor(V*I/P),M[1]=0,g[0]=P/I,g[127]=V/I,h[0]=1,h[127]=_Mathexp(-0.5*V*V);for(var B=126;1<=B;B--)V=_Mathsqrt(-2*_Mathlog(F/V+_Mathexp(-0.5*V*V))),M[B+1]=_Mathfloor(V*I/D),D=V,h[B]=_Mathexp(-0.5*V*V),g[B]=V/I})(),this.next=function(){let I=T(),V=127&I,D=_Mathabs(I)<M[V]?I*g[V]:S(I,V);return D*l+o}};