numpy.random.mtrand.RandomState.chisquare¶

RandomState.chisquare(df, size=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.

Parameters :

df : int

Number of degrees of freedom.

size : tuple of ints, int, optional

Size of the returned array. By default, a scalar is returned.

Returns :

output : ndarray

Samples drawn from the distribution, packed in a size-shaped array.

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:

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

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,

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

References

NIST/SEMATECH e-Handbook of Statistical Methods

Examples

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

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