The McDonald Normal Distribution

TL;DR

The paper introduces the McDonald normal distribution, a flexible five-parameter model that encompasses several existing distributions, providing new analytical tools and demonstrating its applicability through real data fitting.

Contribution

It defines the new McDonald normal distribution, derives its moments and properties, and shows its usefulness in modeling data with three real-world applications.

Findings

Contains normal, skew-normal, and other distributions as special cases

Provides explicit formulas for moments and order statistics

Successfully fits real data demonstrating practical utility

Abstract

A five-parameter distribution called the McDonald normal distribution is defined and studied. The new distribution contains, as special cases, several important distributions discussed in the literature, such as the normal, skew-normal, exponentiated normal, beta normal and Kumaraswamy normal distributions, among others. We obtain its ordinary moments, moment generating function and mean deviations. We also derive the ordinary moments of the order statistics. We use the method of maximum likelihood to fit the new distribution and illustrate its potentiality with three applications to real data.