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: 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:
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
NIST/SEMATECH e-Handbook of Statistical Methods
Examples
>>> np.random.chisquare(2,4) array([ 1.89920014, 9.00867716, 3.13710533, 5.62318272])