Different Estimation Methods for New Probability Distribution Approach Based on Environmental and Medical Data

In this article, we introduce a new extension of the power Lomax (PLo) model by combining the type II exponentiated half-logistic class of statistical models and the PLo model. The new suggested statistical model called type II exponentiated half-logistic-PLo (TIIEHL-PLo) model. However, the new TIIEHL-PLo model is more flexible and applicable than the PLo model and some extensions of THE PLo model, especially those in environmental and medical fields. Some general statistical properties of the TIIEHL-PLo model are computed. Six different estimation approaches, namely maximum likelihood (ML), least-square (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cramér–von Mises (CVM), and Anderson–Darling (AD) estimation approaches, are utilized to estimate the parameters of the TIIEHL-PLo model. The simulation experiment examines the accuracy of the model parameters by employing six different methodologies of estimation. In this study, we analyze three real datasets from the environmental and medical fields to highlight the relevance and adaptability of the proposed approach. The newly suggested model is exceptionally adaptable and outperforms several well-known statistical models