A flexible moment exponential distribution based on confluent hypergeometric functions: properties, inference, and applications

Neveka M. Olmos; Wilson E. Caimanque; Yolanda M. Gómez; Francisco Segovia; Osvaldo Venegas; Neveka M. Olmos; Wilson E. Caimanque; Yolanda M. Gómez; Francisco Segovia; Osvaldo Venegas

doi:10.3934/math.20261108

AIMS Mathematics

2026, Volume 11, Issue 9: 27706-27727. doi: 10.3934/math.20261108

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A flexible moment exponential distribution based on confluent hypergeometric functions: properties, inference, and applications

1.
Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
2.
Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1531772, Chile
3.
Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
4.
Facultad de Ingeniería, Universidad del Desarrollo, Santiago 7610658, Chile
5.
Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile

Received: 05 May 2026 Revised: 11 July 2026 Accepted: 17 July 2026 Published: 01 September 2026
MSC : 62E15, 62F12, 62P30

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.
- moment exponential distribution,
- Kurtosis,
- maximum likelihood estimation,
- Slash distribution,
- EM algorithm
Citation: Neveka M. Olmos, Wilson E. Caimanque, Yolanda M. Gómez, Francisco Segovia, Osvaldo Venegas. A flexible moment exponential distribution based on confluent hypergeometric functions: properties, inference, and applications[J]. AIMS Mathematics, 2026, 11(9): 27706-27727. doi: 10.3934/math.20261108

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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.

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