使用(python)Scipy拟合伽玛分布

Question

任何人都可以帮助我在python中安装gamma分布吗？好吧,我有一些数据:X和Y坐标,我想找到适合这种分布的伽玛参数...在Scipy doc中,事实证明,拟合方法实际存在,但我不知道如何使用它:s ..首先,参数"data"必须采用哪种格式,如何提供第二个参数(参数),因为那是我正在寻找的？

Answer 1

生成一些伽玛数据:

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

在这里,我们将数据拟合到伽玛分布:

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)

Answer 2

我对 ss.gamma.rvs-function 不满意，因为它可以生成负数，这是 gamma 分布不应该有的东西。因此，我通过期望值 = mean(data) 和方差 = var(data) 拟合样本（有关详细信息，请参阅维基百科）并编写了一个函数，该函数可以在没有 scipy 的情况下生成伽马分布的随机样本（我发现很难正确安装，旁注）：

import random
import numpy

data = [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 average
mean_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 sample
grs = [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]