Abstract

GHORBANPOUR, S.  and  CHINIPARDAZ, R.. Form-Invariance of the Non-Regular Exponential Family of Distributions. Rev.Colomb.Estad. [online]. 2018, vol.41, n.2, pp.157-172. ISSN 0120-1751.  https://doi.org/10.15446/rce.v41n2.62233.

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.

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

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