EM algorithm in the slashed inverse Rayleigh regression model with an application

Héctor W. Gómez; Diego I. Gallardo; Marcelo Bourguignon; Osvaldo Venegas; Héctor W. Gómez; Diego I. Gallardo; Marcelo Bourguignon; Osvaldo Venegas

doi:10.3934/math.2026938

AIMS Mathematics

2026, Volume 11, Issue 7: 23262-23281. doi: 10.3934/math.2026938

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EM algorithm in the slashed inverse Rayleigh regression model with an application

1.
Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
2.
Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
3.
Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078-970, RN, Brazil
4.
Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile

Received: 23 May 2026 Revised: 08 July 2026 Accepted: 14 July 2026 Published: 30 July 2026
MSC : 62E15, 62F12, 62P99

This paper introduced a novel distribution that generalized the inverse Rayleigh (IR) distribution. The proposed construction arose from the ratio of two independent random variables: one following the IR distribution and the other a beta distribution. Such a formulation yielded a more flexible model than the baseline IR distribution. We derived key distributional properties, proposed a regression model for the mean, and developed an expectation-maximization (EM) algorithm for maximum likelihood estimation. The finite-sample performance of the estimators was assessed via Monte Carlo simulations, and the practical utility of the model was illustrated through an application to real data.
- inverse Rayleigh distribution,
- slash distribution,
- maximum likelihood,
- quadratic variance function,
- EM algorithm
Citation: Héctor W. Gómez, Diego I. Gallardo, Marcelo Bourguignon, Osvaldo Venegas. EM algorithm in the slashed inverse Rayleigh regression model with an application[J]. AIMS Mathematics, 2026, 11(7): 23262-23281. doi: 10.3934/math.2026938

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Abstract

This paper introduced a novel distribution that generalized the inverse Rayleigh (IR) distribution. The proposed construction arose from the ratio of two independent random variables: one following the IR distribution and the other a beta distribution. Such a formulation yielded a more flexible model than the baseline IR distribution. We derived key distributional properties, proposed a regression model for the mean, and developed an expectation-maximization (EM) algorithm for maximum likelihood estimation. The finite-sample performance of the estimators was assessed via Monte Carlo simulations, and the practical utility of the model was illustrated through an application to real data.

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