A Discrete Power Distribution

TL;DR

This paper introduces a new discrete distribution that serves as an analogue to the two-sided power distribution, capable of modeling diverse shapes and with thoroughly studied properties and parameter estimation methods.

Contribution

It proposes a novel discrete distribution with flexible shape properties, extending the two-sided power distribution to discrete data and analyzing its statistical characteristics.

Findings

Distribution can assume various shapes including bathtub, rectangular, and triangular.

Derived moments and reliability properties of the distribution.

Parameter estimation methods have been developed and analyzed.

Abstract

A new discrete distribution has been proposed as a discrete analogue of the two sided power distribution [Van Drop, J. R. and Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation, Journal of the Royal Statistical Society, Series D (The Statistician), 51, 1: 63-79]. This probability mass function and hazard rate function of this distribution can assume a variety of shapes including bath tub, rectangular, trapezoidal, triangular, J, inverse J, U inverse U, strictly decreasing and strictly increasing shapes. Its moment and reliability properties along with parameter estimation have been investigated.