chisquare(df, size=None, dtype=None, device=None)

Draw samples from a chi-square distribution.

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.

  • df (float or ndarray 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.

  • dtype ({'float16', 'float32', 'float64'}, optional) – Data type of output samples. Default is ‘float32’.

  • device (Device, optional) – Device context of output. Default is current device.


out – Drawn samples from the parameterized chi-square distribution 1.

Return type

ndarray or scalar


ValueError – When df <= 0 or when an inappropriate size is given.


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

\[Q = \sum_{i=0}^{\mathtt{df}} X^2_i\]

is chi-square distributed, denoted

\[Q \sim \chi^2_k.\]

The probability density function of the chi-squared distribution is

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

where \(\Gamma\) is the gamma function,

\[\Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt.\]



NIST “Engineering Statistics Handbook”


>>> np.random.chisquare(2,4)
array([ 1.89920014,  9.00867716,  3.13710533,  5.62318272]) # random