Improving Statistical Model through the Development of Exponentiated Generalized Exponential Pareto Distribution.

Abstract

Most importantly, the derivation of novel class of probability distributions plays a vital role in improving the underlying structure to model complex real-world data. In this study, we propose a new distribution, Exponentiated Generalized Exponential Pareto Distribution (EGEPD), which is a compounding distribution of the Exponentiated Generalized  (EG) class of distribution and Exponential Pareto distribution. The valuation of EGEPD is contemplated by colossal comparisons with other distributions such as Exponential Pareto Distribution (EPD), Exponentiated Exponential Pareto Distribution (EEPD) and Exponential Distribution (ED). EGEPD significantly outperforms these distributions according to both visual and statistical analyses. The EGEPD outperforms all alternatives in terms of Log-Likelihood values, as well as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) scores, confirming its goodness-of-fit and optimal complexity. Goodness-of-fit tests based on Kolmogorov-Smirnov (KS), Anderson-Darling (AD), and Cramér-von Mises (CM) statistics, etc., confirm EGEPD’s performance due to the smallest statistics and the largest p-values that contribute to strong fitting of EGEPD with observed data. Parameter analysis indicates EGEPD’s location parameter (α) adjusts the distribution’s central tendency, while the scale parameter β controls spread and variability. The shape parameters such as a, b, and θ are able to control skewness, tail behavior, and spread of the distribution, allowing the EGEPD to be flexible and fit diverse data characteristics. The ability to adjust this prior flexibility allows for EGEPD to be an effective spatio-temporal model for complex datasets across many domains that require varying spatial and temporal scales of location, variability, or shape. The EGEPD is the best and most robust model with respect to the fitted data and the structure of the data. It proves to be a great addition among other statistical modeling approaches such as the case with Exponential Distribution and also with the medium generators such as EPD and EEPD.

Keywords: Heavy-tailed data, Goodness-of-fit tests, Log-Likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Kolmogorov-Smirnov Statistic, Anderson-Darling Statistic, Cramér-von Mises Statistic, Flexible probability distributions.