Method of logarithmic moments for estimating the gamma-exponential distribution parameters

The article discusses a modified method of moments for estimating the parameters of gamma-exponential distribution. The strong consistency of the estimates obtained is proved. Gamma-exponential distribution is a convenient mechanism for modeling the processes and phenomena using scale mixtures of generalized gamma distributions. Such problems arise in many fields of science under the assumption that the considered parameters are randomized and can be described in terms of Bayesian balance models. The obtained results can be applied in a wide class of problems that use for modeling the distribution with positive unlimited support, without additional assumptions about the representation of the studied object in terms of a scale mixture, due to the wide variety of density types of the five-parameter gamma-exponential distribution.