A generalization for two-sided power distributions and adjusted method of moments

A new rich class of generalized two-sided power (TSP) distributions, where their density functions are expressed in terms of the Gauss hypergeometric functions, is introduced and studied. In this class, the symmetric distributions are supported by finite intervals and have normal shape densities. Our study on TSP distributions also leads us to a new class of discrete distributions on {0, 1, …, k}. In addition, a new numerical method for parameter estimation using moments is given.     

Characterizations of arcsin and related distributions based on a new generalized unimodality

A general characterization for α-unimodal distributions was provided in [Alamatsaz, M.H. 1985: A Note on an Article by Artikis, Acta Mathematica Hungarica 45, 159–162] and its extension to a multivariate case in [Alamatsaz, M.H. 1993: On Characterizations of Exponential and Gamma Distributions, Statistics and Probability Letters 17, 315–319]. Here, by solving the related equations, another generalization for unimodality is presented. As a result of this generalization, a simpler proof of a conjecture, as well as a characterization for generalized arcsin distributions and some generalizations of the author’s earlier works, is obtained. Last, but not the least, it is shown that some elementary methods can be more powerful than some more advanced techniques.