Limit Distributions for the Estimates of the Digamma Distribution Parameters Constructed from a Random Size Sample

In this paper, we study a new type of distribution that generalizes distributions from the gamma and beta classes are widely used in applications. The estimators for parameters digamma obtained by method logarithmic cumulants considered. Based on previously proved asymptotic normality characteristic index shape scale constructed fixed-size sample, obtain statement about convergence these to mixtures normal law case random sample size. Using result, confidence intervals estimated constructed. A number examples limit laws sizes with special forms negative binomial given. results paper can be probabilistic models based continuous an unbounded non-negative support.