How to get the equations for Probability distribution function and Cumulative density function of a gamma distribution in scipy (Python)

Question

Just as we can write the CDF and PDF of a random variable X, following a normal distribution, with its parameters - std and mean using scipy in the following manner:

from numpy import sqrt, pi, exp
mean, std = 295, 250

# defining Cumulative density function
def cdf(x):
    cdf_eqn = lambda t: (1 / (std * sqrt(2 * pi))) * exp(-(((t - mean) ** 2) / (2 * std ** 2)))
    cdf = quad(cdf_eqn, -np.inf, x)[0]
    return cdf

# defining Probability distribution function
def pdf(x):
    return (1 / (std * sqrt(2 * pi))) * exp(-(((x - mean) ** 2) / (2 * std ** 2)))

How can I define the CDF and PDF of a gamma distribution in the same way above?

score 1 · Answer 1 · answered Jun 16 '20 at 07:08

1

You can code the PDF and CDF according to the definition of the gamma distribution:

Source: https://en.wikipedia.org/wiki/Gamma_distribution

You can choose the alpha and beta parameters. Alternatively, you can use the scipy.stats.gamma package.

answered Jun 16 '20 at 07:08

digital_hog

202
1
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Vishal Anand · Accepted Answer · 2020-06-16T18:08:23.207

0

Found out how to do it:

from scipy.stats import gamma

mean = 259
std = 250

x = 100

alpha = ( mean / std)**2
beta = std**2 / mean


def pdf(x,aplha,beta):
  return gamma.pdf(x, a = alpha, scale = beta)

def cdf(x,alpha,beta):
  return gamma.cdf(x, a = alpha, scale = beta)

edited Jun 16 '20 at 18:08

answered Jun 16 '20 at 08:28

Vishal Anand

178
2
10

2

Are you sure that you can use the same gamma.pdf function to get the cdf of the gamma distribution? – digital_hog Jun 16 '20 at 13:11
1

@digital_hog thanks for the correction. Changed the .pdf to .cdf – Vishal Anand Jun 16 '20 at 15:41

How to get the equations for Probability distribution function and Cumulative density function of a gamma distribution in scipy (Python)

2 Answers2