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

• Autores: S. Ghorbanpour, R. Chinipardaz
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 41, Nº. 2, 2018, págs. 157-172
• Idioma: inglés
• DOI: 10.15446/rce.v41n2.62233
• Títulos paralelos:
  • Distribuciones de forma invariante de la familia exponencial no regular
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen 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.

  • English

    Abstract 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.

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