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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.41 no.2 Bogotá July/Dec. 2018 

Artículos originales de investigación

Form-Invariance of the Non-Regular Exponential Family of Distributions

Distribuciones de forma invariante de la familia exponencial no regular

S. Ghorbanpour1  a  , R. Chinipardaz1  b 

1 Department of Statistics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran.


The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that are called the form-invariant weighted distribution. In this paper, by identifying a general class of weight functions, we introduce an extended class of form-invariant weighted distributions belonging to the non-regular exponential family which included two common families of distribution: exponential family and non-regular family as special cases. Some properties of this class of distributions such as the su-cient and minimal su-cient statistics, maximum likelihood estimation and the Fisher information matrix are studied.

Key words: Fisher information matrix; Form-invariance; Non-regular exponential family; Maximum likelihood estimation; Weighted distribution


Las distribuciones ponderadas son usadas cuando el mecanismo de muestreo registra observaciones de acuerdo a una función no negativa. En ocasiones la forma de la función ponderada es igual a la original, excepto, posiblemente, en un cambio de parámetros y se denominan distribuciones ponderadas de forma invariante. En este artículo identificamos una clase general de funciones ponderadas e introducimos una forma extendida de distribuciones ponderadas de forma invariante, la cual incluye dos familias comunes: la familia exponencial y la familia no regular como caso particular. Algunas propiedades de estas distribuciones como las estadísticas suficientes y máximas suficientes, la estimación de máxima verosimilitud y la matriz de información de Fisher son estudiadas.

Palabras-clave: distribución ponderada; estimación de máxima verosimilitud; familia exponencial no regular; invarianza de forma; matriz de información de Fisher

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Received: January 2017; Accepted: January 2018

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