`numpy.random._generator:Generator.chisquare`

Signature

def chisquare ( df , size = None )

Summary

Draw samples from a chi-square distribution.

Extended Summary

When df independent random variables, each with standard normal distributions (mean 0, variance 1), are squared and summed, the resulting distribution is chi-square (see Notes). This distribution is often used in hypothesis testing.

Parameters

df : float or array_like of floats: Number of degrees of freedom, must be > 0.
size : int or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if df is a scalar. Otherwise, np.array(df).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized chi-square distribution.

Raises

: ValueError: When df <= 0 or when an inappropriate size (e.g. size=-1) is given.

Notes

The variable obtained by summing the squares of df independent, standard normally distributed random variables:

Q = i = 1 \sum df X_{i}^{2}

is chi-square distributed, denoted

Q \sim χ_{k}^{2} .

The probability density function of the chi-squared distribution is

p (x) = \frac{( 1/2 ) ^{k /2}}{Γ ( k /2 )} x^{k /2 - 1} e^{- x /2},

where $Γ$ is the gamma function,

Γ (x) = \int_{0}^{- \infty} t^{x - 1} e^{- t} d t .

Examples

rng = np.random.default_rng()

✓

rng.chisquare(2,4)

✗

The distribution of a chi-square random variable with 20 degrees of freedom looks as follows:

import matplotlib.pyplot as plt
import scipy.stats as stats
s = rng.chisquare(20, 10000)
count, bins, _ = plt.hist(s, 30, density=True)
x = np.linspace(0, 60, 1000)

✓

plt.plot(x, stats.chi2.pdf(x, df=20))
plt.xlim([0, 60])

✗

plt.show()

✓

Aliases

numpy.random.Generator.chisquare