Topp-Leone-heavy-tailed-odd log-logistic-G family of distributions with applications

In this study, we introduce a new family of distributions called the Topp-Leone-heavy-tailed-odd log-logistic-G (TL-HT-OLL-G) family of distributions. The primary aim of this research is to propose a versatile statistical tool capable of modeling diverse data behaviors. Several statistical properties including hazard rate function, quantile function, moments, stochastic ordering, distribution of the order statistics and Rényi entropy are discussed. To estimate the parameters of the TL-HT-OLL-G family of distributions, six different estimation methods were employed: maximum likelihood, least-squares, weighted least-squares, Cramér-von Mises, Anderson–Darling, and Right-Tail Anderson-Darling. The consistency of these estimation techniques was evaluated through Monte Carlo simulations, focusing on a specific case within the TL-HT-OLL-G family of distributions. Finally, we illustrate the goodness-of-fit of the new family of distributions by fitting it to two real data sets from different fields. This research highlights the potential of the TL-HT-OLL-G family to provide better fits and insights compared to existing distributions, thereby addressing challenges in statistical modeling and data analysis.