numpy.random.
chisquare
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.
Note
New code should use the chisquare method of a default_rng() instance instead; see random-quick-start.
default_rng()
Number of degrees of freedom, must be > 0.
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.
(m, n, k)
m * n * k
None
df
np.array(df).size
Drawn samples from the parameterized chi-square distribution.
When df <= 0 or when an inappropriate size (e.g. size=-1) is given.
size=-1
See also
Generator.chisquare
which should be used for new code.
Notes
The variable obtained by summing the squares of df independent, standard normally distributed random variables:
System Message: WARNING/2 (Q = \sum_{i=0}^{\mathtt{df}} X^2_i )
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is chi-square distributed, denoted
System Message: WARNING/2 (Q \sim \chi^2_k. )
The probability density function of the chi-squared distribution is
System Message: WARNING/2 (p(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}, )
where
System Message: WARNING/2 (\Gamma)
System Message: WARNING/2 (\Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt. )
References
NIST “Engineering Statistics Handbook” https://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]) # random
