<!DOCTYPE html>
<html lang="en-US">
<head>
<meta charset="utf-8"/>
<title>B4P Reference</title>
<link rel="stylesheet" href="styles.css">
</head>
<div class="wrapper">
<div class="logo">
<a href="index.html">
<img src="Images/B4P_Logo.png" alt="B4P">
</a>
</div>
<div class="header">
<h3>quantile ...</h3>
<a accesskey="p" href="LIB_Function_average.html"><span>Prev</span></a> <a accesskey="n" href="LIB_Function_covariance.html"><span>Next</span></a>
</div>
<section>
<div class="nav">
<div class="booktitle_field"><a style="color:white;" href="LIB_Features_Function_Library.html">Function Library</a></div>
<ul>
<li class="navi"><a href="LIB_Features_Table_of_Contents.html"><div class="navi"> Table of Contents </div></a></li>
<li class="navi"><a href="LIB_Features_Function_Library.html"><div class="navi"> Function Library </div></a></li>
<li class="navi"><a href="LIB_Features_Control_flow_functions.html"><div class="navi">+ Control Flow Functions </div></a></li>
<li class="navi"><a href="LIB_Features_Console_I_O_Functions.html"><div class="navi">+ Console I/O Functions </div></a></li>
<li class="navi"><a href="LIB_Features_Type_Conversion_Functions.html"><div class="navi">+ Type Conversion and Formatting </div></a></li>
<li class="navi"><a href="LIB_Features_Mathematics_and_Statistics.html"><div class="navi"+>- Mathematics and Statistics </div></a></li>
<li class="navi"><ul>
<li class="navi"><a href="LIB_Features_basic_math_functions.html"><div class="navi">+ Basic Math Functions </div></a></li>
<li class="navi"><a href="LIB_Features_transcendental_functions.html"><div class="navi">+ Transcendental Functions </div></a></li>
<li class="navi"><a href="LIB_Features_series_functions.html"><div class="navi">+ Series Functions </div></a></li>
<li class="navi"><a href="LIB_Features_matrix_functions.html"><div class="navi">+ Matrix Functions </div></a></li>
<li class="navi"><a href="LIB_Features_statistics_functions.html"><div class="navi"+>- Statistics Functions </div></a></li>
<li class="navi"><ul>
<li class="navi"><a href="LIB_Function_average.html"><div class="navi"> Basic Statistics Functions </div></a></li>
<li class="navi"><a href="LIB_Function_quantile.html"><div class="navi navi-selected"> quantile ... </div></a></li>
<li class="navi"><a href="LIB_Function_covariance.html"><div class="navi"> covariance, correlation </div></a></li>
<li class="navi"><a href="LIB_Function_gini.html"><div class="navi"> gini Coefficient Functions </div></a></li>
<li class="navi"><a href="LIB_Function_regression.html"><div class="navi"> Linear and Exponential Regression </div></a></li>
<li class="navi"><a href="LIB_Function_linear_interpolation.html"><div class="navi">+ Interpolation Functions </div></a></li>
<li class="navi"><a href="LIB_Function_histogram.html"><div class="navi"> histogram </div></a></li>
</ul></li>
<li class="navi"><a href="LIB_Function_sum_if.html"><div class="navi"> Conditional Combination Functions </div></a></li>
<li class="navi"><a href="LIB_Features_finance_functions.html"><div class="navi">+ Finance and Business Functions </div></a></li>
</ul></li>
<li class="navi"><a href="LIB_Features_string_functions.html"><div class="navi">+ String Functions </div></a></li>
<li class="navi"><a href="LIB_Features_date_and_time_functions.html"><div class="navi">+ Date and Time Functions </div></a></li>
<li class="navi"><a href="LIB_Features_Set_functions.html"><div class="navi">+ Set Functions </div></a></li>
<li class="navi"><a href="LIB_Features_table_functions.html"><div class="navi">+ Table Functions </div></a></li>
<li class="navi"><a href="LIB_Features_variables_functions.html"><div class="navi">+ Variables Functions </div></a></li>
<li class="navi"><a href="LIB_Features_directory_and_file_system_functions.html"><div class="navi">+ Directory and File System Functions </div></a></li>
<li class="navi"><a href="LIB_Features_system_functions.html"><div class="navi">+ System Functions </div></a></li>
<li class="navi"><a href="LIB_Features_help_and_support_functions.html"><div class="navi">+ Help and Support Functions </div></a></li>
<li class="navi"><a href="LIB_Features_Cross-functional_info.html"><div class="navi">+ Cross-Functional Info </div></a></li>
<li class="navi"><div> </div></li>
<li class="navi"><div> <br><br><hr> </div></li>
<li class="navi"><a href="GUI_Features_User_Guide.html"><div class="navi"> User Guide </div></a></li>
<li class="navi"><a href="LAN_Features_Language_Guide.html"><div class="navi"> Language Guide </div></a></li>
<li class="navi"><a href="TAB_Features_Processing_Tables_and_Big_Data.html"><div class="navi"> Table Processing </div></a></li>
<li class="navi"><div> <br><hr> </div></li>
<li class="navi"><a href="LIB_Features_Index.html"><div class="navi"> Index </div></a></li>
</ul>
</div>
<div class="article">
<h4> Function Names</h4>
<div class="white_background_color" ><code>quantile, quantile ignore zero</code></div>
<h4> Description</h4>
<p>
Quantiles are points in a distribution that relate to the rank order of values in that distribution. As an example, the middle
quantile (quantile parameter <i>p</i> = 0.5) is referred as <a class="bold_text" href="LIB_Function_average.html">median</a>() function. B4P also supports this function directly.
Quantile calculation is the inverse of the empirical probability distribution. Following calculation rule is applied:
<br><br>
<i>n</i> refers to the number numeric values provided. <i>p</i> is referred as the quantile parameter.
<br/><img src="Images/Function_quantile_formula.jpg" alt="Quantile formula"><br/>
<br>
Examples:
</p><ul class="bullets"><li class="bullets">For the 1st quartile, use <i>p</i> = 0.25
</li><li class="bullets">For the 2nd quartile (median), use <i>p</i> = 0.5, or the <a class="bold_text" href="LIB_Function_average.html">median</a>() function
</li><li class="bullets">For the 3rd quartil, use <i>p</i> = 0.75
</li></ul><p>
The function <b>quantile ignore zero</b> ignores all zero values provided. If the sequence of values does only contain zeros,
then an exception will be asserted because the quantile cannot be calculated.
</p>
<h4> Call as: <span class="black_text">function</span></h4>
<h4> Parameter count</h4>
<p>2</p>
<h4> Parameters</h4>
<table class="simple"><col style = "width:80px"><col style = "width:120px"><col style = "width:800px"><tr><th>No.</th><th>Type</th><th>Description</th></tr>
<tr><td>1<br/>input</td>
<td>numeral</td>
<td><b>Quantile parameter</b><br/><p>The value must lie between 0 and 1.</p>
</td></tr>
<tr><td>2<br/>input</td>
<td>set</td>
<td><b>Set of values</b><br/><p>The set must contain at least one numeric element which will be included in the calculation. Blank strings are tolerated (no exceptions asserted) and ignored as well (not treated as zero). The values do not need to be ordered in ascending order. This function will take of it.</p>
</td></tr>
<tr><td>Opt. 3<br/>input</td>
<td>numeral</td>
<td><b>Starting set element to include</b><br/><p>Points to the starting set element. <a class="bold_text" href="LAN_Features_negative_indexing.html">Negative indexing</a> is allowed here, i.e. -1 refers to last element in the set.</p>
<span class="black_text"><b> Default value: </b></span>0
</td></tr>
<tr><td>Opt. 4<br/>input</td>
<td>numeral</td>
<td><b>Ending set element to include</b><br/><p>Points to the ending set element. <a class="bold_text" href="LAN_Features_negative_indexing.html">Negative indexing</a> is allowed here, i.e. -1 refers to last element in the set.</p>
<span class="black_text"><b> Default value: </b></span>Last value
</td></tr>
</table>
<h4> Return value</h4>
<table class="simple"><col style = "width:120px"><col style = "width:880px"><tr><th>Type</th><th>Description</th></tr>
<tr>
<td>numeral</td>
<td><b>Calculated quantile</b><br/><p></p></td></tr>
</table>
<h4> Exceptions</h4>
<p>Quantile parameter not between 0 and 1<br/>
No numbers available to calculate</p>
<h4> Examples</h4>
<div class="code_background_color" ><code> ps[] = { 0, 0.0001, 0.1, 0.2, 0.25, 1/3, 0.5, 2/3, 0.75, 0.8, 0.9, 0.9999, 1.0 };<br/>
<br/>
for all( ps[], p[] )<br/>
{<br/>
echo("p: ", p[]," quantile = ", quantile( p[], { 1, 2, 2, 3, 5, 8, 9, 12, 12, 13 } ) );<br/>
}<br/>
echo( "Call with 4 parameters: ", quantile( 0.5, { 8,7,6,5,4,3,2,1 }, 1, 3 ) );<br/>
// Values 7,6,5 are calculated and result in 6.</code></div>
<h4> Output</h4>
<div class="output_background_color" ><code>p: 0 quantile = 1<br>p: 0.0001 quantile = 1<br>p: 0.1 quantile = 1.5<br>p: 0.2 quantile = 2<br>p: 0.25 quantile = 2<br>p: 0.3333333333 quantile = 3<br>p: 0.5 quantile = 6.5<br>p: 0.6666666667 quantile = 9<br>p: 0.75 quantile = 12<br>p: 0.8 quantile = 12<br>p: 0.9 quantile = 12.5<br>p: 0.9999 quantile = 13<br>p: 1.0 quantile = 13<br>Call with 4 parameters: 6<br></code></div><u>Try it yourself:</u> Open <b>LIB_Function_quantile.b4p</b> in <a class="bold_text" href="B4P_Examples.zip">B4P_Examples.zip</a>. Decompress before use.
<h4> See also</h4>
<p><a class = "bold_text" href="LIB_Function_average.html">median</a></p>
</div>
</section>
<div class="footer">
Copyright (C) 2007 - 2024 Georg A. zur Bonsen, All Rights Reserved
</div>
</div>
</html>