# numpy.random.Generator.standard_gamma

method

random.Generator.standard_gamma(shape, size=None, dtype=np.float64, out=None)

  Draw samples from a standard Gamma distribution.

  Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated “k”) and scale=1.

  Parameters
    shape float or array_like of floats

      Parameter, must be non-negative.

    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 `shape` is a scalar. Otherwise, `np.array(shape).size` samples are drawn.

    dtype dtype, optional

      Desired dtype of the result, only `float64` and `float32` are supported. Byteorder must be native. The default value is np.float64.

    out ndarray, optional

      Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values.

  Returns
    out ndarray or scalar

      Drawn samples from the parameterized standard gamma distribution.

  See also

  `scipy.stats.gamma`

    probability density function, distribution or cumulative density function, etc.

  Notes

  The probability density for the Gamma distribution is

  \[p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},\]

  where \(k\) is the shape and \(\theta\) the scale, and \(\Gamma\) is the Gamma function.

  The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.

  References

  1

    Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html

  2

    Wikipedia, “Gamma distribution”, https://en.wikipedia.org/wiki/Gamma_distribution

  Examples

  Draw samples from the distribution:

      >>> shape, scale = 2., 1. # mean and width
      >>> s = np.random.default_rng().standard_gamma(shape, 1000000)

  Display the histogram of the samples, along with the probability density function:

      >>> import matplotlib.pyplot as plt
      >>> import scipy.special as sps
      >>> count, bins, ignored = plt.hist(s, 50, density=True)
      >>> y = bins**(shape-1) * ((np.exp(-bins/scale))/
      ...                       (sps.gamma(shape) * scale**shape))
      >>> plt.plot(bins, y, linewidth=2, color='r')
      >>> plt.show()

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