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
gamma method of a
instance instead; see random-quick-start.
The shape of the gamma distribution. Must be non-negative.
The scale of the gamma distribution. Must be non-negative. Default is equal to 1.
Output shape. If the given shape is, e.g.,
(m, n, k), then
m * n * k samples are drawn. If size is
a single value is returned if
scale are both scalars.
np.broadcast(shape, scale).size samples are drawn.
Drawn samples from the parameterized gamma distribution.
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()