A New Flexible Model: The Half Logistic Topp-Leone Kumaraswamy Fréchet Distribution with Applications to Biomedical Data

Abstract

This paper introduces a novel statistical model named the Half Logistic Topp-Leone Kumaraswamy Fréchet (HLTLKw-F) distribution, constructed by compounding the half logistic family of distributions with the Topp-Leone Kumaraswamy Fréchet distribution. The proposed model exhibits a highly flexible hazard function, making it suitable for a wide range of lifetime data. Several mathematical properties of the HLTLKw-F distribution are derived, including the survival function, quantile function, order statistics, entropy, and moment generating function. The model parameters are estimated using three classical estimation methods: maximum likelihood estimation, the Anderson–Darling method, and the Cramér–von Mises method. A comprehensive simulation study is conducted to evaluate the consistency and reliability of the estimators, demonstrating their effectiveness across different sample sizes. The practical applicability of the HLTLKw-F distribution is illustrated through its application to three real-life biomedical datasets, where it outperforms existing competing models based on various goodness-of-fit measures.