Type-I Heavy-Tailed Topp-Leone Family of Distributions with Applications to Biomedical Data

Abstract

In this study, a new family of probability distributions is proposed by integrating the tail flexibility of the Type I Heavy Tail family and the Topp Leone generated family of distributions and this is called the Type I Heavy Tailed Topp-Leone Generated (TIHTTL-G) family of distributions. The significant statistical properties of the TIHTTL-G family of distributions such as moments, generating functions, order statistics, stochastic ordering, and Rényi entropy are derived. The estimation of the parameters of a specific sub-model, the TIHTTL-Rayleigh (TIHTTLR), is performed employing ten different estimation techniques, both classical and Bayesian. Bayesian estimators are derived under three different loss functions namely: Square Error Loss Function, Linear Exponential Loss Function and Generalized Entropy Loss Function. Simulation experiments was conducted to examine parameter estimators from the different estimation procedures. Finally, to demonstrate the applicability of the proposed family, the TIHTTLR was fitted to three real-life datasets, and the results show its superior fit compared to competing models.