scipy.stats.chi¶

scipy.stats.chi = <scipy.stats._continuous_distns.chi_gen object>[source]¶

A chi continuous random variable.

As an instance of the rv_continuous class, chi object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Notes

The probability density function for chi is:

\[f(x, df) = \frac{x^{df-1} \exp(-x^2/2)}{2^{df/2-1} \gamma(df/2)}\]

for \(x > 0\).

Special cases of chi are:

chi(1, loc, scale) is equivalent to halfnorm

chi(2, 0, scale) is equivalent to rayleigh

chi(3, 0, scale) is equivalent to maxwell

chi takes df as a shape parameter.

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, chi.pdf(x, df, loc, scale) is identically equivalent to chi.pdf(y, df) / scale with y = (x - loc) / scale.

Examples

>>> from scipy.stats import chi
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>> df = 78
>>> mean, var, skew, kurt = chi.stats(df, moments='mvsk')

Display the probability density function (pdf):

>>> x = np.linspace(chi.ppf(0.01, df),
...                 chi.ppf(0.99, df), 100)
>>> ax.plot(x, chi.pdf(x, df),
...        'r-', lw=5, alpha=0.6, label='chi pdf')

Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed.

Freeze the distribution and display the frozen pdf:

>>> rv = chi(df)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of cdf and ppf:

>>> vals = chi.ppf([0.001, 0.5, 0.999], df)
>>> np.allclose([0.001, 0.5, 0.999], chi.cdf(vals, df))
True

Generate random numbers:

>>> r = chi.rvs(df, size=1000)

And compare the histogram:

>>> ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

Methods

`rvs(df, loc=0, scale=1, size=1, random_state=None)`	Random variates.
`pdf(x, df, loc=0, scale=1)`	Probability density function.
`logpdf(x, df, loc=0, scale=1)`	Log of the probability density function.
`cdf(x, df, loc=0, scale=1)`	Cumulative distribution function.
`logcdf(x, df, loc=0, scale=1)`	Log of the cumulative distribution function.
`sf(x, df, loc=0, scale=1)`	Survival function (also defined as `1 - cdf`, but sf is sometimes more accurate).
`logsf(x, df, loc=0, scale=1)`	Log of the survival function.
`ppf(q, df, loc=0, scale=1)`	Percent point function (inverse of `cdf` — percentiles).
`isf(q, df, loc=0, scale=1)`	Inverse survival function (inverse of `sf`).
`moment(n, df, loc=0, scale=1)`	Non-central moment of order n
`stats(df, loc=0, scale=1, moments='mv')`	Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
`entropy(df, loc=0, scale=1)`	(Differential) entropy of the RV.
`fit(data, df, loc=0, scale=1)`	Parameter estimates for generic data.
`expect(func, args=(df,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)`	Expected value of a function (of one argument) with respect to the distribution.
`median(df, loc=0, scale=1)`	Median of the distribution.
`mean(df, loc=0, scale=1)`	Mean of the distribution.
`var(df, loc=0, scale=1)`	Variance of the distribution.
`std(df, loc=0, scale=1)`	Standard deviation of the distribution.
`interval(alpha, df, loc=0, scale=1)`	Endpoints of the range that contains alpha percent of the distribution