The McDonald Normal Distribution
Methodology
2022-06-03 v1 Statistics Theory
Data Analysis, Statistics and Probability
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2206.00763,
title = {The McDonald Normal Distribution},
author = {G. M. Cordeiro and R. J. Cintra and L. C. Rêgo},
journal= {arXiv preprint arXiv:2206.00763},
year = {2022}
}
Comments
27 pages, 13 figures