Distribution of the sum of gamma mixture random variables
Masato Kitani, Hidetoshi Murakami, Hiroki Hashiguchi · SUT Journal of Mathematics · 2024
Mixture distributions are extensively used to model data in practical analysis. Several researchers in various scientific fields have considered the gamma mixture distribution. Moreover, the gamma mixture distribution includes important distributions, such as gamma, exponential, chi-squared, and Lindley distributions. Herein, we discuss the probability density function and cumulative distribution function of the sum of independent and non-identically (inid) distributed gamma mixture random variables. Thereafter, we obtain the exact distribution of the sum of the inid-distributed gamma mixture random variables using simple infinite incomplete gamma series. In the numerical study, we calculate the percentiles of the sum of generalized Lindley random variables, which is the special case of the sum of the gamma mixture. Numerical studies show that the sum of gamma mixture is advantageous in the real data analysis.