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Characterizations of non-normalized discrete probability distributions and their application in statistics

Betsch, S. 1; Ebner, B. 1; Nestmann, F. 1
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)

Abstract:

From the distributional characterizations that lie at the heart of Stein’s method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop tools for the solution of statistical problems. Our characterizations, and hence the applications built on them, do not require any knowledge about normalization constants of the probability laws. To demonstrate that our statistical methods are sound, we provide comparative simulation studies for the testing of fit to the Poisson distribution and for parameter estimation of the negative binomial family when both parameters are unknown. We also consider the problem of parameter estimation for discrete exponential-polynomial models which generally are non-normalized.


Verlagsausgabe §
DOI: 10.5445/IR/1000143615
Veröffentlicht am 11.03.2022
Originalveröffentlichung
DOI: 10.1214/22-EJS1983
Scopus
Zitationen: 8
Web of Science
Zitationen: 8
Dimensions
Zitationen: 13
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2022
Sprache Englisch
Identifikator ISSN: 1935-7524
KITopen-ID: 1000143615
Erschienen in Electronic Journal of Statistics
Verlag Institute of Mathematical Statistics (IMS)
Band 16
Heft 1
Seiten 1303-1329
Nachgewiesen in Dimensions
Web of Science
Scopus
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