numpy.random.chisquare¶

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:

Parameters:	df : int or array_like of ints Number of degrees of freedom. 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.

df : int or array_like of ints

Number of degrees of freedom.

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:

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

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])