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Home  >  Transactions of NAMP VOL 14

18. ON THEORETICAL STUDY OF RAYLEIGH-EXPONENTIATED ODD GENERALIZED-X FAMILY OF DISTRIBUTIONS by A. Yahaya and S. I. S. Doguwa Volume 14, (January - March, 2021 Issue)
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ON THEORETICAL STUDY OF RAYLEIGH-EXPONENTIATED ODD GENERALIZED-X FAMILY OF DISTRIBUTIONS

A. Yahaya and S. I. S. Doguwa

Department of Statistics, Ahmadu Bello University, Zaria, Nigeria

Abstract

Over the years, several attempts were made by many researchers, to improve the goodness-of-fit of numerous classical probability distributions by inducing additional parameters aimed at enhancing their flexibility in describing datasets from diverse fields of human endeavour. In this article, a new variant of T-Exponentiated Odd Generalized-X family of distributions introduced in an earlier research is presented. The new variant titled Rayleigh-Exponentiated Odd Generalized-X family becomes what it is, when the variable T follows Rayleigh distribution. Some important functions comprising the cumulative distribution, probability density, survival function and the hazard function of the new sub-family are presented. Other vital derivations include moments, moment generating function, quantile function, entropy and function of order statistics. Furthermore, the proposed sub-family is shown to belong to the Exponentiated-G family of distributions. The method of maximum likelihood is used to derive estimates of the unknown parameters; after which parameter asymptotic confidence bounds were also obtained.

Keywords: T-X family, Exponentiated-G family, Parameter induction, Order statistics, Maximum likelihood Estimation

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