Probability Laws Derived from the Euler Gamma Function: Understanding through Case Studies

Abstract

Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euleur functions. Application of the functions of Euler contributed to and facilitated the obtaining of important results in statistics and especially in the theories of distribution of sampling. Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. This study aims to understand the Euler Gamma Function and its associated laws of probabilities or probability distributions derived from the function gamma. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euler functions.