Type I Half-Logistic Exponentiated Kumaraswamy Distribution With Applications

Abstract

This study introduces the Type I Half-Logistic Exponentiated Kumaraswamy (TIHLEtKw) distribution, a new statistical model designed to provide improved flexibility and accuracy for data modelling across diverse applications. The background of the study highlights the limitations of existing distributions in capturing complex real-world data patterns. The purpose of this work is to develop and characterize the TIHLEtKw distribution, deriving key properties such as the moment generating function, reliability function, hazard function, and quantile function. Additionally, order statistics were explored to understand the behavior of the distribution. Simulation studies demonstrated the efficiency of the maximum likelihood estimators (MLEs) for the parameters of the TIHLEtKw distribution, with mean square error (MSE) values decreasing as sample size increased, indicating the estimators’ consistency. For example, for a parameter set (α = 2, β = 1.5, γ = 1, δ = 2), the MSE decreased from 0.045 for a sample size of 50 to 0.011 for a sample size of 300. The application of the TIHLEtKw distribution to real datasets, including civil engineering data with a skewness of 2.18 and wind speed data with a kurtosis of 3.62, demonstrated its superior fit compared to other models. Metrics such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) indicated that the TIHLEtKw distribution outperformed established models like the Kumaraswamy-Kumaraswamy and Weibull-Kumaraswamy distributions, with reductions in AIC of up to 15%. The findings confirm the TIHLEtKw distribution's effectiveness in capturing data variability and complexity, offering a robust tool for statistical modelling. The study concludes that this distribution significantly enhances modelling capabilities, and it is recommended for use in fields such as environmental studies, biomedicine, and finance. Future research could focus on extending the model's applications and optimizing computational methods for parameter estimation.