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

Q3 Mathematics

Revista Colombiana De Estadistica Pub Date : 2018-07-01 DOI:10.15446/RCE.V41N2.62233

S. Ghorbanpour, R. Chinipardaz, S. M. R. Alavi

引用次数: 0

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 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.

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非正则指数分布族的形式-不变性

当抽样机制根据非负权函数记录观测值时，使用加权分布。有时，加权分布的形式与原始分布相同，除非参数可能发生变化，即所谓的形式不变加权分布。本文通过识别一类一般的权函数，引入了一类属于非正则指数族的形式不变权分布的扩展，作为特例，它包含了指数族和非正则族两个常见的分布族。研究了这类分布的充分统计量和最小充分统计量、极大似然估计和Fisher信息矩阵等性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Revista Colombiana De Estadistica STATISTICS & PROBABILITY-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Colombian Journal of Statistics publishes original articles of theoretical, methodological and educational kind in any branch of Statistics. Purely theoretical papers should include illustration of the techniques presented with real data or at least simulation experiments in order to verify the usefulness of the contents presented. Informative articles of high quality methodologies or statistical techniques applied in different fields of knowledge are also considered. Only articles in English language are considered for publication. The Editorial Committee assumes that the works submitted for evaluation have not been previously published and are not being given simultaneously for publication elsewhere, and will not be without prior consent of the Committee, unless, as a result of the assessment, decides not publish in the journal. It is further assumed that when the authors deliver a document for publication in the Colombian Journal of Statistics, they know the above conditions and agree with them.