Mathematical and statistical structures of a new generalized probability distribution for fitting different types of datasets

Authors

Mahmoud El-Morshedy, Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia\\ Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptFollow

Abstract

This article presents a novel approach to modeling a heavily tailed continuous distribution known as the logarithmic slash model. This model is built upon the transformation Y = eX , where X follows the slash distribution. Our aim is to introduce a model with desirable characteristics for practical applications, drawing inspiration from the unique features of the logarithmic model. As a result, we develop both univariate and multivariate extensions of the logarithmic slash model and conduct a thorough exploration of its mathematical properties. We employ the maximum likelihood method to estimate the model parameters and conduct simulation studies to assess the biases and mean square errors of these estimators. One of the primary concerns addressed by the logarithmic slash model is its ability to effectively accommodate various types of data. To demonstrate its versatility, we utilize a range of datasets and compare the performance of the logarithmic slash model to a strong competitor in terms of data fit. The results clearly indicate that the logarithmic slash model outperforms its competitor, highlighting its efficacy in handling different types of data.

Recommended Citation

El-Morshedy, Mahmoud (2023) "Mathematical and statistical structures of a new generalized probability distribution for fitting different types of datasets," Information Sciences Letters: Vol. 12 : Iss. 12 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol12/iss12/21