Modeling Heavy-Tailed Data via the New Topp-Leone Heavy-Tailed Gompertz-G Family of Distributions

Thatayaone  Moakofi; Olivia  Atutey; Broderick  Oluyede; Huybrechts  F. Bindele

Authors

Thatayaone Moakofi Department of Statistics, University of Botswana, Gaborone, Botswana
Olivia Atutey Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama, USA
Broderick Oluyede Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana
Huybrechts F. Bindele Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama, USA

Keywords:

Topp-Leone-G, heavy-tailed, Gompertz-G, estimation methods, simulations, applications

Abstract

In this article, we introduce a new distribution named, Topp-Leone Heavy-Tailed GompertzG (TL-HT-Gom-G) family of distributions. Several mathematical and statistical properties of the new TL-HT-Gom-G family of distributions including quantile function, moments, moment generating function, Renyi entropy, distribution of order statistics, stochastic orderings are derived. Risk ´measures and a numerical simulation study are also presented for this family of distributions. To estimate the model parameters, we use six different estimation methods, namely, maximum likelihood, Anderson-Darling, Right-Tail Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, and Cramer-von Mises. A simulation study is further performed to assess these estimation techniques ´and finally we demonstrate the applicability of the new family of distributions using applications to three real data sets.

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