Fitting a gamma distribution with (python) Scipy

Generate some gamma data:

import scipy.stats as stats    alpha = 5loc = 100.5beta = 22data = stats.gamma.rvs(alpha, loc=loc, scale=beta, size=10000)    print(data)# [ 202.36035683  297.23906376  249.53831795 ...,  271.85204096  180.75026301#   364.60240242]

Here we fit the data to the gamma distribution:

fit_alpha, fit_loc, fit_beta=stats.gamma.fit(data)print(fit_alpha, fit_loc, fit_beta)# (5.0833692504230008, 100.08697963283467, 21.739518937816108)print(alpha, loc, beta)# (5, 100.5, 22)

I was unsatisfied with the ss.gamma.rvs-function as it can generate negative numbers, something the gamma-distribution is supposed not to have. So I fitted the sample through expected value = mean(data) and variance = var(data) (see wikipedia for details) and wrote a function that can yield random samples of a gamma distribution without scipy (which I found hard to install properly, on a sidenote):

import randomimport numpydata = [6176, 11046, 670, 6146, 7945, 6864, 767, 7623, 7212, 9040, 3213, 6302, 10044, 10195, 9386, 7230, 4602, 6282, 8619, 7903, 6318, 13294, 6990, 5515, 9157]# Fit gamma distribution through mean and averagemean_of_distribution = numpy.mean(data)variance_of_distribution = numpy.var(data)def gamma_random_sample(mean, variance, size):    """Yields a list of random numbers following a gamma distribution defined by mean and variance"""    g_alpha = mean*mean/variance    g_beta = mean/variance    for i in range(size):        yield random.gammavariate(g_alpha,1/g_beta)# force integer values to get integer samplegrs = [int(i) for i in gamma_random_sample(mean_of_distribution,variance_of_distribution,len(data))]print("Original data: ", sorted(data))print("Random sample: ", sorted(grs))# Original data: [670, 767, 3213, 4602, 5515, 6146, 6176, 6282, 6302, 6318, 6864, 6990, 7212, 7230, 7623, 7903, 7945, 8619, 9040, 9157, 9386, 10044, 10195, 11046, 13294]# Random sample:  [1646, 2237, 3178, 3227, 3649, 4049, 4171, 5071, 5118, 5139, 5456, 6139, 6468, 6726, 6944, 7050, 7135, 7588, 7597, 7971, 10269, 10563, 12283, 12339, 13066]

If you want a long example including a discussion about estimating or fixing the support of the distribution, then you can find it in https://github.com/scipy/scipy/issues/1359 and the linked mailing list message.

Preliminary support to fix parameters, such as location, during fit has been added to the trunk version of scipy.