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## Print version ISSN 1409-2433

### Rev. Mat vol.28 n.2 San José Jul./Dec. 2021

#### http://dx.doi.org/10.15517/rmta.v28i2.44507

Artículo

A moment recursive formula for a class of distributions

Una fórmula recursiva para los momentos de algunas distribuciones de probabilidad

Abstract

We provide a recursive formula for the computation of moments of distributions belonging to a subclass of the exponential family. This subclass includes important cases as the binomial, negative binomial, Poisson, gamma and normal distribution, among others. The recursive formula provides a procedure to sequentially calculate the moments using only elementary operations. The approach makes no use of the moment generating function.

Keywords: moments; exponential family; recursive formula.

Resumen

Se proporciona una fórmula recursiva para calcular los momentos de ciertas distribuciones que pertenecen a una subclase de la familia exponencial. A esta subclase de distribuciones pertenecen las distribuciones binomial, binomial negativa, Poison, gama y normal, entre otras. La fórmula recursiva provee de un procedimiento para calcular los momentos de manera secuencial usando únicamente operaciones elementales. El método no hace uso de la función generadora de momentos.

Palabras clave: momentos; familia exponencial; fórmula recursiva.

Mathematics Subject Classification: 60E05, 97K50, 97K60.

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Acknowledgments

Thanks to the referees for their constructive and valuable observations that allowed an improvement of the manuscript.

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Received: November 16, 2020; Revised: February 26, 2021; Accepted: April 19, 2021