Some probability-statistical properties of the gamma-exponential distribution

Currently, much attention of researchers is paid to generalizations of well-known mathematical objects in order to obtain adequate models describing real phenomena. An important role in the applied theory of probability and mathematical statistics is played by the gamma class of distributions, which has proven to be a convenient and effective tool for modeling a lot of real processes. The gamma class is quite wide and includes distributions that have such useful properties as, for example, infinite divisibility and stability, which makes it possible to use distributions from this class as asymptotic approximations in various limit theorems. One of the most important tasks of applied statistics is to obtain estimates of the parameters of the model distribution from the available real data. The paper considers the gamma-exponential distribution which is a generalization of the distributions from the gamma class. Estimates and asymptotic confidence intervals are given for some parameters of this distribution. The problems of computer modeling of sample realizations from the gamma-exponential distribution and the numerical estimation of parameters for the sample are discussed. The results of the work can be widely used in the study of probabilistic models based on continuous distributions with an unbounded nonnegative support.