Title: Modelling cancer data using a new generalised type II Topp-Leone heavy-tailed type II exponentiated half logistic-G family of distributions

Authors: Peter T. Chinofunga; Broderick Oluyede; Fastel Chipepa

Addresses: Department of Mathematics and Statistical Sciences, School of Pure and Applied Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana; Department of Mathematics and Computer Science, School of Natural Sciences, Great Zimbabwe University, P. Bag 135, Masvingo, Zimbabwe ' Department of Mathematics and Statistical Sciences, School of Pure and Applied Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana ' Department of Mathematics and Statistical Sciences, School of Natural Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana

Abstract: In this paper, a novel generalised family of distributions (FoD), the type II Topp-Leone heavy-tailed type II exponentiated half logistic-G (TIITL-HT-TIIEHL-G) distribution is developed. Some statistical properties of this new FoD which include the quantile function, order statistics, Rényi entropy, stochastic ordering, moment of residual and reversed residual life are derived. Through Monte Carlo simulations, the maximum likelihood estimation method outperforms alternative techniques namely weighted least squares, least squares, Cramér-von Mises, and Anderson Darling in estimating the type II-Topp-Leone heavy-tailed type II-exponentiated-half-logistic-Weibull (TIITL-HT-TIIEHL-W) distribution, a special case of the TIITL-HT-TIIEHL-G FoD parameters. The distribution is used to illustrate the flexibility of this new FoD using two real life datasets.

Keywords: type II Topp-Leone distribution; heavy-tailed distribution; type II exponentiated half logistic distribution; moments; maximum likelihood estimation.

DOI: 10.1504/IJMMNO.2025.146322

International Journal of Mathematical Modelling and Numerical Optimisation, 2025 Vol.15 No.2, pp.137 - 167

Received: 03 Dec 2024
Accepted: 16 Mar 2025
Published online: 21 May 2025 *

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