flopscope.numpy.random.RandomState.chisquare

fnp.random.RandomState.chisquare(self, df, size=None)

Draw samples from a chi-square distribution.

Adapted from NumPy docs np.random.RandomState.chisquare

Arearandom

Typecounted

NumPy Refnp.random.RandomState.chisquare

Cost

\text{numel}(\text{output})

Flopscope Context

Legacy chi-square sampler; cost = numel(output).

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.

Note.

New code should use the chisquare method of a Generator instance instead; please see the random-quick-start.

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, flops.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=1}^{\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

footnote

1

NIST "Engineering Statistics Handbook"
https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

Examples

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