Harris extended inverted Kumaraswamy distribution: Properties and applications to COVID-19 data

Statistical probability distributions are frequently used in real-world data analysis. However, data from fields such as environmental science, finance, and biomedical sciences may not always fit in classical distributions. This usually requires the development of new distributions that better reflect data behavior in a variety of situations. In this paper, we introduce a new four-parameter distribution termed the Harris extended inverted Kumaraswamy (HEIK) distribution is proposed and analyzed in detail. This generalization accommodates well-known submodels including MOEIK, GIK, EIK, IK and MOLL as observed in this study. The study includes the basic properties of the observed probabilistic model. Explicit expressions for major mathematical properties of this distribution such as quantile function, complete moments, incomplete moments, conditional moments, inverted moments, mean deviation, moment generating function, inequality measure, mean residual life and mean inactivity time are derived. The various entropy measures, extropy and order statistics are derived. The maximum likelihood estimation method is used to estimate the parameters. Simulation studies are conducted for different parameter values and compare the performance of the HEIK distribution. Three illustrative examples involving COVID-19 datasets from three countries are presented.