Two-sided Power Distribution Research Articles

Generalizations of Two-Sided Power Distributions and Their Convolution

A general form of a family of bounded two-sided continuous distributions is introduced. The uniform and triangular distributions are possibly the simplest and best known members of this family. We also describe families of continuous distribution on a bounded interval generated by convolutions of these two-sided distributions. Examples of various forms of convolutions of triangular distributions are presented and analyzed.

A versatile bivariate distribution on a bounded domain: Another look at the product moment correlation

The Farlie-Gumbel-Morgenstern (FGM) family has been investigated in detail for various continuous marginals such as Cauchy, normal, exponential, gamma, Weibull, lognormal and others. It has been a popular model for the bivariate distribution with mild dependence. However, bivariate FGMs with continuous marginals on a bounded support discussed in the literature are only those with uniform or power marginals. In this paper we study the bivariate FGM family with marginals given by the recently proposed two-sided power (TSP) distribution. Since this family of bounded continuous distributions is very flexible, the properties of the FGM family with TSP marginals could serve as an indication of the structure of the FGM distribution with arbitrary marginals defined on a compact set. A remarkable stability of the correlation between the marginals has been observed.

The Standard Two-Sided Power Distribution and its Properties

This article discusses a family of distributions which would seem not to receive proper attention in the literature. The two-parameter distribution is introduced with an application in the financial engineering domain. Special cases of this family include the triangular distribution, the standard power function distribution, and the uniform distribution. Properties of the distribution are investigated and the maximum likelihood estimation procedure for its two parameters is derived. The flexibility of the family as compared to that of the beta family is discussed.