Fixed point characterizations of continuous univariate probability distributions and their applications

By extrapolating the explicit formula of the zero-bias distribution occurring in the context of Stein’s method, we construct characterization identities for a large class of absolutely continuous univariate distributions. Instead of trying to derive characterizing distributional transformations that...

Full description

Saved in:
Bibliographic Details
Published in:Annals of the Institute of Statistical Mathematics 2021-02, Vol.73 (1), p.31-59
Main Authors: Betsch, Steffen, Ebner, Bruno
Format: Article
Language:English
Subjects:
Distribution functions
Economics
Finance
Goodness of fit
Insurance
Management
Mathematics
Mathematics and Statistics
Statistics
Statistics for Business
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:By extrapolating the explicit formula of the zero-bias distribution occurring in the context of Stein’s method, we construct characterization identities for a large class of absolutely continuous univariate distributions. Instead of trying to derive characterizing distributional transformations that inherit certain structures for the use in further theoretic endeavors, we focus on explicit representations given through a formula for the density- or distribution function. The results we establish with this ambition feature immediate applications in the area of goodness-of-fit testing. We draw up a blueprint for the construction of tests of fit that include procedures for many distributions for which little (if any) practicable tests are known. To illustrate this last point, we construct a test for the Burr Type XII distribution for which, to our knowledge, not a single test is known aside from the classical universal procedures.
ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-019-00735-1