py25. Gamma Distribution in Python

Like the Poisson and Exponential distribution, the Gamma distribution is also dependent on the exponential series.

Besides the calculation above, we can use the function scipy.stats.gamma.cdf

# ex25.py
from __future__ import print_function, division
import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import gamma
# shape, scale parameters
k,s = 7,2

def get_num(x,kv):
    xp = x/s
    coeff = np.exp(-xp)
    if kv == 0: return coeff
    cv = xp/np.arange(1,kv+1)
    return coeff*np.prod(cv)

def gamma_dis(x, calc):
    dis_calc = np.zeros(len(x))
    for i in range(len(x)):
        S = [get_num(x[i],kv) for kv in range(k)]
        dis_calc[i] = 1 - sum(S)
    dis_R = gamma.cdf(x, k, scale = s)
    if calc: return dis_calc
    else: return dis_R

main = ('Gamma Cumulative Distribution Function'
        '\nShape = 7, Scale = 2')
x = np.arange(40, step = .1)
plt.plot(x, gamma_dis(x,False),'r')
plt.xlabel('x')
plt.ylabel('P')
plt.title(main)
plt.plot(x, gamma_dis(x,True), 'b')
plt.show()

Output: