A method for estimating parameters of the gamma-exponential distribution from a sample with weakly dependent components

The article proves the asymptotic normality of the estimators for the gamma-exponential distribution parameters obtained using the modified method of moments in the case of a weak dependence of the sample components. For the estimators of the bent and scale parameters of the gamma-exponential distribution with fixed shape and concentration parameters, the central limit theorem is proved in the case when the maximum correlation coefficient between the sample elements tends to zero. The proof is based on the study of the sample spectral density and the results of the theory of stationary random sequences. The results of the article can be used to substantiate the asymptotic normality of the estimators for the parameters of the digamma distribution, the particular types of which include the generalized gamma distribution and the generalized beta distribution of the second kind that arise when describing processes modeled with distributions having a nonnegative unbounded support.