A method for estimating bent, shape and scale parameters of the gamma-exponential distribution

The article discusses a modified method of moments for estimating three of five parameters of the gamma-exponential distribution. It is proposed to estimate the distribution parameters based on its logarithmic moments. An explicit form of estimates of the bent, shape, and scale parameters is given for fixed concentration parameters of the gamma-exponential distribution; the strong consistency of the obtained estimates is justified. The article also discusses the method of eliminating unnecessary solutions to the system of equations for logarithmic article moments; a number of numerical examples are presented to illustrate the derivation of estimates from model samples. Since the analyzed distribution is closely related to the generalized gamma distribution and the generalized beta distribution of the second kind, the results of this work can be widely used in applied problems using continuous distributions with an unbounded nonnegative support for modeling.