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Univariate and bivariate extensions of the generalized exponential distributions

Univariate and bivariate extensions of the generalized exponential distributions AbstractThe main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematica Slovaca de Gruyter

Univariate and bivariate extensions of the generalized exponential distributions

Mathematica Slovaca , Volume 71 (6): 18 – Dec 20, 2021

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Publisher
de Gruyter
Copyright
© 2021 Mathematical Institute Slovak Academy of Sciences
ISSN
0139-9918
eISSN
1337-2211
DOI
10.1515/ms-2021-0073
Publisher site
See Article on Publisher Site

Abstract

AbstractThe main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

Journal

Mathematica Slovacade Gruyter

Published: Dec 20, 2021

Keywords: Bivariate geometric generalized exponential distribution; discrete generalized exponential distribution; EM algorithm; generalized exponential distribution; maximum likelihood estimators; univariate geometric generalized exponential distribution; Primary 62F10; Secondary 62H10

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