A flexible moment exponential distribution based on confluent hypergeometric functions: properties, inference, and applications
Journal
AIMS Mathematics
Date Issued
2026
Author(s)
Olmos, Neveka M.
Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
University of Atacama
Gómez, Yolanda M.
Segovia, Francisco
Venegas, Osvaldo
Abstract
In this paper, we introduced a novel extension of the moment exponential (ME) distribution using a confluent hypergeometric construction. The proposed model was developed through a slash-type mechanism to provide greater flexibility in modeling kurtosis. We derived the general form of the probability density function and study several of its statistical properties, including moments, skewness, and kurtosis coefficients. Statistical inference was conducted using both the method of moments and maximum likelihood estimation, the latter implemented via the expectation-maximization (EM) algorithm. A simulation study was performed to evaluate the finite-sample performance of the maximum likelihood estimators. Finally, the proposed model was applied to real datasets exhibiting high kurtosis, showing improved fitting performance compared to the classical ME distribution.


