Modeling environmental datasets using a type II half-logistic exponentiated Kumaraswamy distribution

Abstract In the field of environmental science, data characteristics often exhibit significant variability, challenging the applicability of classical probability distributions for environmental data modeling. In this paper, we introduced a novel four-parameter distribution called the type II half-logistic exponentiated Kumaraswamy (TIIHLEKw) distribution, derived from the type II half-logistic exponentiated generalized family of distributions and using the Kumaraswamy distribution as the baseline. This distribution exhibits greater flexibility compared to the traditional Kumaraswamy distribution. Importantly, the TIIHLEKw distribution offers symmetrical, right-skewed, left-skewed, unimodal, J-shaped, and reversed J-shaped densities and various hazard functions, including increasing, decreasing, bathtub, and J-shaped forms. These patterns exhibited by the distribution make it particularly useful for modeling environmental datasets. Basic properties of the TIIHLEKw distribution, such as moments, moment generating function, quantile function, hazard function, survival function, Renyi entropy, skewness, kurtosis, and distribution of order statistics, are derived. Unknown parameters of the distribution are estimated using the maximum likelihood approach, and the performance of maximum likelihood estimator is assessed through Monte Carlo simulations. Finally, three applications to real data on measurements of burr (in millimeters), measurements taken from petroleum rock samples in a petroleum reservoir, and Senegal's COVID-19 mortality rates for 31 days, from July 18, 2021, to August 17, 2021, are evaluated to demonstrate the importance of the TIIHLEKw model over other extended versions of the Kumaraswamy models. The empirical findings suggest that the TIIHLEKw model outperforms other extended versions of the Kumaraswamy models in these applications.