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

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.