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2020•Journal of the Egyptian Mathematical SocietyOpen access

The T–R {Y} power series family of probability distributions

Patrick Osatohanmwen, Francis O. Oyegue, Sunday M. Ogbonmwan

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Abstract

Abstract A new family of univariate probability distributions called the T − R {Y} power series family of probability distributions is introduced in this paper by compounding the T − R {Y} family of distributions and the power series family of discrete distributions. A treatment of the general mathematical properties of the new family is carried out and some sub-families of the new family are specified to depict the broadness of the new family. The maximum likelihood method of parameter estimation is suggested for the estimation of the parameters of the new family of distributions. A special member of the new family called the Gumbel–Weibull–{logistic}–Poisson (GUWELOP) distribution is defined and found to exhibit both unimodal and bimodal shapes. The GUWELOG distribution is further applied to a real multi-modal data set to buttress its applicability.

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Abstract A new family of univariate probability distributions called the T − R {Y} power series family of probability distributions is introduced in this paper by compounding the T − R {Y} family of distributions and the power series family of discrete distributions. A treatment of the general mathematical properties of the new family is carried out and some sub-families of the new family are specified to depict the broadness of the new family. The maximum likelihood method of parameter estimation is suggested for the estimation of the parameters of the new family of distributions. A special member of the new family called the Gumbel–Weibull–{logistic}–Poisson (GUWELOP) distribution is defined and found to exhibit both unimodal and bimodal shapes. The GUWELOG distribution is further applied to a real multi-modal data set to buttress its applicability.

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Available abstract

Abstract A new family of univariate probability distributions called the T − R {Y} power series family of probability distributions is introduced in this paper by compounding the T − R {Y} family of distributions and the power series family of discrete distributions. A treatment of the general mathematical properties of the new family is carried out and some sub-families of the new family are specified to depict the broadness of the new family. The maximum likelihood method of parameter estimation is suggested for the estimation of the parameters of the new family of distributions. A special member of the new family called the Gumbel–Weibull–{logistic}–Poisson (GUWELOP) distribution is defined and found to exhibit both unimodal and bimodal shapes. The GUWELOG distribution is further applied to a real multi-modal data set to buttress its applicability.

Key concepts: Mathematics, Series (stratigraphy), Gumbel distribution, Poisson distribution, Natural exponential family, Weibull distribution, Univariate, Exponential family

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