A new characterization of the Gamma distribution and associated goodness of fit tests

We propose a class of weighted \(L_2\)-type tests of fit to the Gamma distribution. Our novel procedure is based on a fixed point property of a new transformation connected to a Steinian characterization of the family of Gamma distributions. We derive the weak limits of the statistic under the null...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2018-06
Main Authors: Betsch, Steffen, Ebner, Bruno
Format: Article
Language:English
Subjects:
Computer simulation
Goodness of fit
Monte Carlo simulation
Null hypothesis
Probability distribution functions
Statistical analysis
Statistical tests
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We propose a class of weighted \(L_2\)-type tests of fit to the Gamma distribution. Our novel procedure is based on a fixed point property of a new transformation connected to a Steinian characterization of the family of Gamma distributions. We derive the weak limits of the statistic under the null hypothesis and under contiguous alternatives. Further, we establish the global consistency of the tests and apply a parametric bootstrap technique in a Monte Carlo simulation study to show the competitiveness to existing procedures.
ISSN:2331-8422
DOI:10.48550/arxiv.1806.06028