A new extended mixture normal distribution

Božidar V. Popović; Gauss Cordeiro; Edwin Ortega; Marcelino A.R. Pascoa

Vol. 22 No. 1 (2017)

Regular Articles

A new extended mixture normal distribution

Published 2016-10-17

Božidar V. Popović
Gauss Cordeiro
Edwin Ortega
Marcelino A.R. Pascoa

Božidar V. Popović
University of Montenegro

Gauss Cordeiro
Departamento de Estat´ıstica, Universidade Federal de Pernambuco, Recife

Edwin Ortega
Departamento de Cincias Exatas, Universidade de S˜ao Paulo, Piracicaba

Marcelino A.R. Pascoa
Departamento de Estatstica, Universidade Federal de Mato Grosso, Cuiab

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Abstract

The normal distribution is the most important model in statistics for analysisof continuous data. We propose a new distribution, called the extended mixture normaldistribution, based on a linear mixture model. We obtain explicit expressions for theordinary and incomplete moments, generating and quantile functions, mean deviations andtwo measures of entropy. The method of maximum likelihood and Bayesian are adopted toestimate the model parameters. The proposed distribution can provide better fits to realdata than the normal and other classical distributions as shown by means of one application.

Keywords

Extended normal, Generating function, Mean deviation, Moment, Mixture normal, Normal distribution, Quantile expansion

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