Benefiting from statistical modeling in the analysis of current health expenditure to gross domestic product

In this article, we provide a novel criterion for decision making by addressing the statistical analysis and modeling of health protection expenditures relative to health system of gross domestic product in a comparative study of four different countries, namely the United States, Malaysia, Egypt, and kingdom of Saudi Arabia. Researchers examined the issue of spending on health protection expenditures in relation to gross domestic product from a variety of angles, including social and statistical. Previous statistical studies also addressed the study of statistical modeling through regression approach. Here we study this issue from a different perspective, namely modeling with statistical distributions. In the statistical modeling of the data, we use an extended heavy-tailed updated version of Weibull distribution named the generalized Weibull distribution Weibull (GWD-W) model, which has good statistical properties in terms of flexibility and goodness of fit. Some distributional properties and statistical functions, including the Renyi entropy, skewness, kurtosis, the heavy-tailed behavior, regular variation, and identifiable property are given. Two important actuarial risk measures are derived. A simulation study is conducted to prove the usefulness of the two actuarial measures in finance. The estimation of the model parameters via the maximum likelihood approach is discussed. Comparison study vs some competitive statistical models is performed using the Kolmogorov-Smirnov test for a sample and some detection criteria. The discussion shows that proposed statistical modeling of health care expenditure as a percentage of gross domestic product (GDP) for health care compares well with their peers.