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Mathematical Communications, Vol. 22 No. 1, 2017.

Original scientific paper

A new extended mixture normal distribution

Božidar V. Popović orcid id orcid.org/0000-0001-6349-4843 ; Faculty of Philosophy, University of Montenegro, Nikšić, Montenegro
Gauss Cordeiro ; Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, Brazil
Edwin M. Ortega ; Departamento de Ciências Exatas, Universidade de São Paulo, Brazil
Marcelino Pascoa ; Departamento de Estatística, Universidade Federal de Mato Grosso,Brazil

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Abstract

The normal distribution is the most important model in statistics for analysis of continuous data. We propose a new distribution, called the extended mixture normal distribution, based on a linear mixture model. We obtain explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations and
two measures of entropy. The maximum likelihood and Bayesian methods are used to estimate the model parameters. We prove empirically that the new distribution can be a better model than the normal and other classical distributions by means of an application
to real data.

Keywords

extended normal; generating function; mean deviation; mixture normal; moment; normal distribution; quantile expansion

Hrčak ID:

176716

URI

https://hrcak.srce.hr/176716

Publication date:

4.4.2017.

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