nlcpy.random.Generator.gamma
- Generator.gamma(self, shape, scale=1.0, size=None)
Draws samples from a Gamma distribution.
Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated "k") and scale (sometimes designated "theta"), where both parameters are > 0.
- Parameters
- shapefloat
The shape of the gamma distribution. Must be non-negative.
- scalefloat, optional
The scale of the gamma distribution. Must be non-negative. Default is equal to 1.
- sizeint or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn.
- Returns
- outndarray
Drawn samples from the parameterized gamma distribution.
注釈
The probability density for the Gamma distribution is
where
is the shape and
the scale, and
is the Gamma function.
制限事項
If shape is neither a scalar nor None : NotImplementedError occurs.
If scale is neither a scalar nor None * NotImplementedError occurs.
Examples
Draw samples from the distribution:
>>> import nlcpy as vp >>> shape, scale = 2., 2. # mean=4, std=2*sqrt(2) >>> s = vp.random.default_rng().gamma(shape, scale, 1000)
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.get(), 50, density=True) >>> y = bins**(shape-1)*(vp.exp(-bins/scale)/(sps.gamma(shape)*scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') >>> plt.show()