Topp-Leone Type I Heavy-Tailed - G Power Series Class of Distributions: Properties, Risk Measures, and Applications

  • Wilbert Nkomo 1.Department of Applied Statistics, Manicaland State University of Applied Sciences, Mutare, Zimbabwe. 2.Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana
  • Broderick Oluyede Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana
  • Fastel Chipepa Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana
DOI: https://doi.org/10.19139/soic-2310-5070-2039
Keywords: Topp-Leone, Heavy-tail, Power series distribution, Censoring, Risk measure, Estimation, Moments

Abstract

This study presents a new class of distributions (CoDs) called the Topp-Leone type I heavy-tailed-G power series (TL-HT-GPS),along with its subclass, the Topp-Leone type I heavy-tailed log-logistic power series (TL-HT-LLOGPS) distribution. Statistical properties of this novel CoDs were derived, and actuarial risk measures were developed and numerically simulated.The maximum likelihood estimation technique was employed to estimate the unknown parameters of the model, and Monte Carlo simulations were used to evaluate the estimates' consistency. Through the use of the Topp-Leone type I heavy-tailed log-logistic Poisson (TL-HT-LLOGP) distribution, a special case of the TL-HT-LLOGPS distribution, two real data sets including a censored case, were examined to illustrate the potential of the proposed distribution. The TL-HT-LLOGP distribution was compared to a few selected non-nested competing distributions including some known heavy-tailed distributions and power series distributions. The TL-HT-LLOGP out-performed the contending distributions through various goodness-of-fit tests conducted.

Author Biographies

Broderick Oluyede, Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana
Broderick Oluyede is a former Director of the Statistical Consulting Unit (SCU) in Georgia Southern University's Department of Mathematical Sciences in Statesboro, Georgia, USA.He currently holds the position of Full Professor of Mathematics and Statistics at Botswana International University of Science and Technology (BIUST). He has over thirty years of research and teaching experience at Bowling Green State University, Georgia State University, University of Georgia, Oklahoma State University, Georgia Southern University, and BIUST. Broderick Oluyede has authored and co-authored more than two hundred and sixty (260) research papers. Multivariate, Order Restricted Inference, Stochastic Dependence, and Weighted Distributions are some of his research interests. He serves on the editorial boards of several journals.
Fastel Chipepa, Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana
Fastel Chipepa is a lecturer at the Department of Mathematics and Statistical Sciences,Faculty of Science, Botswana International University of Science and Technology. He has authored and co-authored over fifty (50) research papers. His main areas of interest include distribution theory, survival analysis, biostatistical methods and biometry. He is a member of two editorial boards: Annals of Immunology and Immunotherapy (AII) and International Journal of Mathematics, Statistics and Operations Research.
Published
2024-08-15
How to Cite
Nkomo, W., Oluyede, B., & Chipepa, F. (2024). Topp-Leone Type I Heavy-Tailed - G Power Series Class of Distributions: Properties, Risk Measures, and Applications. Statistics, Optimization & Information Computing, 13(1), 88-110. https://doi.org/10.19139/soic-2310-5070-2039
Issue
Vol 13 No 1 (2025)
Section
Research Articles
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