A novel family of distributions: Properties, inequality measures and applications to socio economic development indicators

In this paper, we focused on two families of distributions: the Topp–Leone Kumaraswamy family and a novel proposed family of distributions. Subsequently, we explore their composition, leading to a novel family of distributions exhibiting compelling features for data modeling. Specifically, we examine a special member of this novel family, employing the inverse exponential distribution as the cumulative density function. We establish the mathematical properties, investigate the moments and the stochastic properties, and propose a parameter estimation method based on the maximum likelihood of the new model. To assess the applicability of our model, we gather data related to development indicators in Benin Republic. Additionally, employing competing models, we analyze some real-life data and compare the results to the novel distribution. Model performance is evaluated in terms of fitting observed data, and we conduct an in-depth interpretation of the outcomes. This study makes a significant contribution by introducing a novel family of distributions tailored for modeling development indicators. The findings of this research may have substantial implications for statistical analysis and decision-making in the context of Benin’s economic and social development.