Gamma Function and Gamma Probability Density Function

Gamma function and Gamma Probability Distribution

Gamma function and Gamma probability density both are very important concepts in mathematics and statistics. Furthermore, understanding Gamma function and Gamma probability density helps to understand chi-square distribution which plays very important role in machine learning. Especially, in Decision Tree Learning Chi-Square distribution used. In this post, I will explain from Gamma function to Gamma probability density function that will help to understand Chi-Square distribution.

Gamma function is defined as improper integral which is

Value of Γ1

Value of  Γ1/2

Gamma probability density function is

Expectation of Random Variable X of Gamma Probability Distribution Function

Variance of Random Variable X of Gamma Probability Density Function

Like,  Poisson Distribution  Gamma probability density function’s random variable has both expectation and variance are equal.