Data driven efficient score tests for Poissonity

Abstract

New data driven score tests for testing goodness of fit of the Poisson distribution are proposed. They are direct applications of the general construction of data driven goodness-of-fit tests for composite hypotheses developed in Inglot et al. 1997. By a simulation study it is shown that these tests perform almost equally well as the best known solutions for standard alternatives and outperform them for more difficult alternatives.

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

“…This is a classical statistical problem, well studied in the literature. Apart from Pearson's χ 2 test, see Khmaladze (2013) for recent developments, the hitherto proposed tests are based on the (conditional) empirical distribution function, see Beltrán-Beltrán and O'Reilly (2019); Gürtler and Henze (2000); Henze (1996); Frey (2012), the empirical probability generating function, see Baringhaus and Henze (1992); Puig and Weiß (2020); Rueda and O'Reilly (1999), on the integrated distribution function, see Klar (1999), on a characterization by mean distance, see Székely and Rizzo (2004), on quadratic forms of score vectors, see Inglot (2019), on Charlier polynomials, see Ledwina and Wylupek (2017), on conditional probabilities ratio, see Beltrán-Beltrán and O'Reilly (2019), and on relating first-and second-order moments, see Kyriakoussis, Li and Papadopoulos (1998). For a survey of classical procedures and a comparative simulation study see Gürtler and Henze (2000).…”

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

“…This is a classical statistical problem, well studied in the literature. Apart from Pearson's χ 2 test, see Khmaladze (2013) for recent developments, the hitherto proposed tests are based on the (conditional) empirical distribution function, see Beltrán-Beltrán and O'Reilly (2019); Frey (2012); Gürtler and Henze (2000); Henze (1996), the empirical probability generating function, see Baringhaus and Henze (1992); Puig and Weiß (2020); Rueda and O'Reilly (1999), on the integrated distribution function, see Klar (1999), on a characterization by mean distance, see Székely and Rizzo (2004), on quadratic forms of score vectors, see Inglot (2019), on Charlier polynomials, see Ledwina and Wylupek (2017), on conditional probabilities ratio, see Beltrán-Beltrán and O'Reilly ( 2019), and on relating first-and second-order moments, see Kyriakoussis et al (1998). For a survey of classical procedures and a comparative simulation study see Gürtler and Henze (2000).…”

A family of consistent normally distributed tests for Poissonity

“…have been proposed for Poissonity (e.g. [11], [1], [15], [4]). Omnibus tests are particularly appealing since they are consistent against all possible alternative distributions but they commonly have a non-trivial asymptotic behaviour.…”