# numpy.random.chisquare

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.

  Note

  New code should use the `chisquare` method of a `Generator` instance instead; please see the 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, `np.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.

  See also

  `random.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:

  \[Q = \sum_{i=0}^{\mathtt{df}} X^2_i\]

  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” 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