This study presents the power Mira distribution, an innovative three-parameter probability model that improves baseline distributions by including an extra shaping parameter. The suggested distribution has exceptional adaptability in representing various data characteristics, such as left and right skewness, declining trends, and unimodal patterns. These characteristics render it exceptionally appropriate for modeling risk-related data, an essential component of actuarial science and insurance analytics. We do an extensive theoretical study, delineating essential statistical features and offering a robust framework for parameter estimation. Critical risk metrics, including value-at-risk and tail value-at-risk, are calculated and assessed using comprehensive numerical simulations, validating the precision and efficacy of the suggested estimators. We illustrate the practical value of the power Mira distribution by applying it to a real-world insurance loss dataset and comparing its performance with established models. The findings underscore its exceptional goodness-of-fit and flexibility, affirming its capability as an effective instrument for risk assessment and financial modeling.

In this work, a new family of distributions referred to as type II exponentiated half-logistic-Gompertz-G (TIIEHL-Gom-G) family of distributions is introduced and studied. Some of the main statistical properties of these family of distributions are derived. The model parameters are estimated using the maximum likelihood estimation technique and consistency of maximum likelihood estimators is evaluated by performing a simulation study. The importance and versatility of the TIIEHL-Gom-G family of distributions is demonstrated in an application to two real data sets from different fields.

This paper aims to develop a new class of distributions, namely, type II exponentiated half-logistic Topp-Leone power series (TIIEHL-TL-GPS) class of distributions. Some important properties including moments, quantiles, moment generating function, entropy and maximum likelihood estimates are derived. A simulation is conducted study to evaluate the consistency of the maximum likelihood estimates. We also present three real data examples to illustrate the usefulness of the new class of distributions. Results shows that the proposed model performs better than nested and several non-nested models on selected data sets

In this paper, we introduce the newly generated Ristić–Balakrishnan–Topp–Leone–Gompertz-G family of distributions. Statistical and mathematical properties of this new family including moments, moment generating function, incomplete moments, conditional moments, probability weighted moments, distribution of the order statistics, stochastic ordering, and Rényi entropy are derived. The unknown parameters of the family are inferred using the maximum likelihood estimation technique. A Monte Carlo simulation study is performed to investigate the convergence of the maximum likelihood estimation. Three real-life data sets are used to demonstrate the flexibility and capacity of the new family of distributions.

In this study, we introduce a new generalized family of distributions called the Exponentiated Half Logistic-Harris-G (EHL-Harris-G) distribution, which extends the Harris-G distribution. The motivation for introducing this generalized family of distributions lies in its ability to overcome the limitations of previous families, enhance flexibility, improve tail behavior, provide better statistical properties and find applications in several fields. Several statistical properties, including hazard rate function, quantile function, moments, moments of residual life, distribution of the order statistics and Rényi entropy are discussed. Risk measures, such as value at risk, tail value at risk, tail variance and tail variance premium, are also derived and studied. To estimate the parameters of the EHL-Harris-G family of distributions, the following six different estimation approaches are used: maximum likelihood (MLE), least-squares (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cramér–von Mises (CVM), and Anderson–Darling (AD). The Monte Carlo simulation results for EHL-Harris-Weibull (EHL-Harris-W) show that the MLE method allows us to obtain better estimates, followed by WLS and then AD. Finally, we show that the EHL-Harris-W distribution is superior to some other equi-parameter non-nested models in the literature, by fitting it to two real-life data sets from different disciplines.

In this study, we propose a new heavy-tailed distribution, namely, the type I heavy-tailed odd power generalized Weibull-G family of distributions. Several statistical properties including hazard rate function, quantile function, moments, distribution of the order statistics and Renyi entropy are presented. Actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are also derived. To obtain the estimates of the parameters of the new family of distributions, we adopt the maximum likelihood estimation method and assess the consistency property via a Monte Carlo simulation. Finally, we illustrate the usefulness of the new family of distributions by analyzing four real life data sets from different fields such as insurance, engineering, bio-medical and environmental sciences.