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The McDonald Normal Distribution

Author(s): Gauss M. Cordeiro | Renato J. Cintra | Leandro C. Rêgo | Edwin M. M. Ortega

Journal: Pakistan Journal of Statistics and Operation Research
ISSN 1816-2711

Volume: 8;
Issue: 3;
Date: 2012;
Original page

Keywords: McDonald normal distribution | Maximum likelihood estimation | Mean deviation | Moment generating function

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.
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