Treffer: A family of consistent normally distributed tests for Poissonity

Title:
A family of consistent normally distributed tests for Poissonity
Authors:
A. Di Noia, M. Marcheselli, C. Pisani, L. Pratelli
Contributors:
Di Noia, A., Marcheselli, M., Pisani, C., Pratelli, L.
Source:
AStA Advances in Statistical Analysis. 108:209-223
Publication Status:
Preprint
Publisher Information:
Springer Science and Business Media LLC, 2023.
Publication Year:
2023
Subject Terms:
05 social sciences, Asymptotics, Consistent test, Normal distribution, Poissonity, Probability generating function, Consistent test, Mathematics - Statistics Theory, Statistics Theory (math.ST), 01 natural sciences, Probability generating function, 0502 economics and business, FOS: Mathematics, 0101 mathematics, Normal distribution, Asymptotics, Poissonity
Document Type:
Fachzeitschrift Article
File Description:
application/pdf
Language:
English
ISSN:
1863-818X
1863-8171
DOI:
10.1007/s10182-023-00478-8
DOI:
10.48550/arxiv.2112.12201
Access URL:
http://arxiv.org/abs/2112.12201
https://hdl.handle.net/11365/1233954
https://doi.org/10.1007/s10182-023-00478-8
https://rdcu.be/dft2m
Rights:
CC BY
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....68894f61d0074071754b80592ad649ab
Database:
OpenAIRE

Weitere Informationen

A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted alternatives to the Poisson distribution. Actually, the family of test statistics is based on the difference between the plug-in estimator of the Poisson cumulative distribution function and the empirical cumulative distribution function. The test statistics have an intuitive and simple form and are asymptotically normally distributed, allowing a straightforward implementation of the test. The finite sample properties of the test are investigated by means of an extensive simulation study. The test shows satisfactory behaviour compared to other tests with known limit distribution.