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Mahdi Rasekhi

Mahdi Rasekhi

Academic rank: Assistant Professor
ORCID:
Education: PhD.
ScopusId:
HIndex:
Faculty: Mathematical Sciences and Statistics
Address:
Phone: 0813-33339843 داخلی 391

Research

Title
The Exponentiated Gompertz Generated Family of Distributions: Properties and Applications
Type
JournalPaper
Keywords
Reliability and life testing, Applications to social sciences, Gompertz distribution, New generator, New Distribution for proportion
Year
2016
Journal Chilean Journal of Statistics
DOI
Researchers Mahdi Rasekhi

Abstract

The proposal of more exible distributions is an activity often required in practical con-texts. In particular, adding a positive real parameter to a probability distribution by exponentiation of its cumulative distribution function has provided exible generated distributions having interesting statistical properties. In this paper, we study general mathematical properties of a new generator of continuous distributions with three extra parameters called the exponentiated Gompertz generated (EGG) family. We present some of its special models as well as an essay on its physical motivation. From math-ematical point of view, we derive explicit expressions of the EGG family: the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Renyi entropies and order statistics, which are valid for any base-line model. We also provide a bivariate EGG extension. The estimation procedure by maximum likelihood of the new class is elaborated and discussed. In order to quantify and to assess the asymptotic behavior of this procedure, we perform a simulation study. Finally, two applications to real data are performed. Results furnish evidence in favor of the use of the EGG beta distribution as a good proposal to these data sets.