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

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 is 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 sufficient and minimal sufficient statistics, maximum likelihood estimation and the Fisher information matrix are studied.

• Autores: Ghorbanpour, Samereh; Chinipardaz, Rahim; Alavi, Seyed Mohammad Reza
• Tipo de recurso: Article of journal
• Fecha de publicación: 2018
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/66484
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/66484; http://bdigital.unal.edu.co/67512/
• Palabra clave: 51 Matemáticas / Mathematics; 31 Colecciones de estadística general / Statistics; Fisher information matrix; Form-invariance; Non-regular exponential family; Maximum likelihood estimation; Weighted distribution; Distribución ponderada; estimación de m\'axima verosimilitud; familia exponencial no regular; invarianza de forma; matriz de información de Fisher
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional