Normal Power Series Class of Distributions: Model, Properties and Applications

TL;DR

This paper introduces the normal power series (NPS) distribution class, combining normal and power series distributions, providing closed-form functions, parameter estimation methods, and practical applications as an alternative to existing skew-normal models.

Contribution

The paper proposes a new NPS distribution class, deriving closed-form density and distribution functions, and develops an EM algorithm for parameter estimation.

Findings

Closed-form density and distribution functions for NPS

Effective EM algorithm for parameter estimation

Applications demonstrating NPS model versatility

Abstract

A new class of distributions, called as normal power series (NPS), which contains the normal one as a particular case, is introduced in this paper. This new class which is obtained by compounding the normal and power series distributions, is presented as an alternative to the class of skew-normal and Balakrishnan skew-normal distributions, among others. The density and distribution functions of this new class of distributions, are given by a closed expression which allows us to easily compute probabilities, moments and related measurements. Estimation of the parameters of this new model by maximum likelihood method via an EM- algorithm is given. Finally, some applications are shown as examples.