The McDonald Normal Distribution

Gauss M. Cordeiro, Renato J. Cintra, Leandro C. Rêgo, Edwin M. M. Ortega

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


McDonald normal distribution; Maximum likelihood estimation; Mean deviation; Moment generating function

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DOI: http://dx.doi.org/10.18187/pjsor.v8i3.510

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Title

The McDonald Normal Distribution

Keywords

McDonald normal distribution; Maximum likelihood estimation; Mean deviation; Moment generating function

Description

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.


Date

2012-07-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 8. No. 3, 2012



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810