numpy.random.chisquare — NumPy v1.11 Manual (original) (raw)

numpy.random.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 : int or tuple of ints, optional Output shape. If the given shape is, e.g., (m, n, k), thenm * n * k samples are drawn. Default is None, in which case a single value 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

[R213]	NIST “Engineering Statistics Handbook”http://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

Examples

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