mars.tensor.random.chisquare#

mars.tensor.random.chisquare(df, size=None, chunk_size=None, gpu=None, dtype=None)[source]#

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 (float or array_like of floats) – Number of degrees of freedom, should 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, mt.array(df).size samples are drawn.

  • chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension

  • gpu (bool, optional) – Allocate the tensor on GPU if True, False as default

  • dtype (data-type, optional) – Data-type of the returned tensor.

Returns

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

Return type

Tensor or scalar

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

1

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

Examples

>>> import mars.tensor as mt

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