gamma(shape, scale=1.0, size=None)¶
Draw 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.
New code should use the
gammamethod of a
default_rng()instance instead; see random-quick-start.
- shapefloat or array_like of floats
The shape of the gamma distribution. Must be non-negative.
- scalefloat or array_like of floats, 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), then
m * n * ksamples are drawn. If size is
None(default), a single value is returned if
scaleare both scalars. Otherwise,
np.broadcast(shape, scale).sizesamples are drawn.
- outndarray or scalar
Drawn samples from the parameterized gamma distribution.
probability density function, distribution or cumulative density function, etc.
which should be used for new code.
The probability density for the Gamma distribution is
where is the shape and the scale, and 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.
Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html
Wikipedia, “Gamma distribution”, https://en.wikipedia.org/wiki/Gamma_distribution
Draw samples from the distribution:
>>> shape, scale = 2., 2. # mean=4, std=2*sqrt(2) >>> s = np.random.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, 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()