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), then
m * 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:
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is chi-square distributed, denoted
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The probability density function of the chi-squared distribution is
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x^{k/2 - 1} e^{-x/2},
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where
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is the gamma function,
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References
NIST/SEMATECH e-Handbook of Statistical Methods
Examples
>>> np.random.chisquare(2,4)
array([ 1.89920014, 9.00867716, 3.13710533, 5.62318272])