Comparing the Methods of Estimators of the Modified Inverted Kumaraswamy Distribution Using Inverse Power Function

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.