Study’s Excerpt: • A new extension of the Modified Inverted Kumaraswamy (MIK) distribution using the inverse power function is introduced. • Maximum likelihood estimation (MLE) and maximum product spacing (MPS) methods were applied, with MPS consistently outperforming MLE. • Simulation results demonstrated that as sample sizes increased, both estimation techniques showed improved accuracy. • The practical utility of the proposed model was validated using two real-life datasets. Full Abstract: This article considers the problem of estimating additional parameters of the modified inverted Kumaraswamy (MIK) distribution using the inverse power function based on the general Kumaraswamy distribution. The parameters' maximum likelihood (MLE) estimators are obtained, while the Bayesian estimates are obtained using the maximum product spacing (MPS). We obtained a new model for generalizing the existing ones to make them more flexible and to aid their application in various fields. An expression for reliability measures, order statistics, and some other important properties are derived. The maximum likelihood estimation method is used to estimate the proposed model's unknown parameters. Finally, a simulation study was reported concerning different sample sizes and method schemes. The practical utility of the proposed distribution is demonstrated using two real-life datasets: (i) survival times (in months) of 101 patients diagnosed with advanced acute myelogenous leukaemia, and (ii) strengths of 63 samples of 1.5 cm glass fibres, originally obtained by workers at the UK National Physical Laboratory. The results highlight the robustness and flexibility of the proposed model in reliability and survival analysis contexts.

In this work, a type II Topp-Leone-G family of distributions is parametrically transformed to create a new flexible family of continuous probability distributions called exponentiated type II Topp-Leone-G distribution through exponentiation. A variety of density shapes and hazard rate behaviors, such as increasing, decreasing, bathtub, inverted bathtub-shaped, and unimodal forms, can be captured by the proposed family, which generalizes several current lifetime models. In addition to discussing significant special cases that correspond to well-known distributions, explicit expressions for the cumulative distribution function, probability density function, survival function, hazard rate function, quantile function, actuarial measures, and linear representation of the probability density function are derived. The maximum likelihood approach is used for parameter estimation, and the simulation study provides a brief discussion of the estimator’s asymptotic characteristics. Kolmogorov–Smirnov and Cramer–Von Mises goodness-of-fit metrics and their p-values, along with information criteria like Akaike Information Criterion, Bayesian Information Criterion, Consistent Akaike Information Criterion, and Hannan–Quinn Information Criterion, are used to evaluate the appropriateness of the model. Furthermore, to visually assess model performance, graphical diagnostic techniques, such as density and distribution function overlays, quantile–quantile plots, and probability–probability plots, are used. Real-life datasets are analyzed to show the applicability of the exponentiated type II Topp-Leone-G family using Weibull distribution as the baseline, and its performance is compared with some other competing distributions. The findings demonstrate the potential utility of the proposed model in the areas of insurance and related applied domains by showing that it fits better than the competing models considered.