Recent Achievements in Modified Chi-Squared Goodness-of-Fit Testing

Voinov, Vassilly; Alloyarova, Roza; Pya, Natalie

doi:10.1007/978-0-8176-4619-6_18

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…The well-known Nikulin-Rao-Robson (NRR) statistic (Y 2 n ( Θ n )) is one of famous modified classical chisquared goodness-of-fit test (GOF), that was introduced by Nikulin [29] and Rao-Robson [31] ( [14,35,36]). It uses the maximum likelihood estimation on the initial data.…”

Section: Nikulin-rao-robson Statistic Test For Complete Datamentioning

confidence: 99%

The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test

Abouelmagd¹,

Hamed²,

Hamedani³

et al. 2019

J. Nonlinear Sci. Appl.

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The goal of this work is to introduce a new family of continuous distributions with a strong physical applications. Some statistical properties are derived, and certain useful characterizations of the proposed family of distributions are presented. Five applications are provided to illustrate the importance of the new family. A modified goodness-of-fit test for the new family in complete data case are investigated via two examples. We propose, as a first step, the construction of Nikulin-Rao-Robson statistic based on chi-squared fit tests for the new family in the case of complete data. The new test is based on the Nikulin-Rao-Robson statistic separately proposed by [

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Section: Nikulin-rao-robson Statistic Test For Complete Datamentioning

confidence: 99%

The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test

Abouelmagd¹,

Hamed²,

Hamedani³

et al. 2019

J. Nonlinear Sci. Appl.

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“…It was subsequently adjusted in (Hadi and Wells, 1990), whose version we employ. Such methodology found applications in the fields of econometrics (Andrews, 1987(Andrews, , 1988Vuong, 1987;Wilson and Koehler, 1991), biology (Marchingo et al, 2016;Zhang, 1999), and statistical theory (Drost, 1989;Tyler, 1981;Voinov et al, 2008).…”

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confidence: 99%

Discrete convolution statistic for hypothesis testing

Prevedello

Duffy

2020

Communications in Statistics - Theory and Methods

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The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In this case, the computation of classical χ 2 statistics, which would not include all observations, results in loss of power, especially when sample sizes are small. Here, as an alternative that uses all data, the nonparametric maximum likelihood estimator for the distribution of sum of discrete and independent random variables, which we call the convolution statistic, is proposed and its limiting normal covariance matrix determined. To challenge null hypotheses about the distribution of this sum, the generalized Wald's method is applied to define a testing statistic whose distribution is asymptotic to a χ 2 with as many degrees of freedom as the rank of such covariance matrix.Rank analysis also reveals a connection with the roots of the probability generating functions associated to the addend variables of the linear models. A simulation study is performed to compare the convolution test with Pearson's χ 2 , and to provide usage guidelines. INTRODUCTIONIn this paper we examine the problem of testing the null hypothesis of equality in distri-

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Wald’s Method and Nikulin-Rao-Robson Test

Voinov¹,

Nikulin²

2013

Chi-Squared Goodness of Fit Tests With Applications

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Recent Achievements in Modified Chi-Squared Goodness-of-Fit Testing

Cited by 5 publications

References 24 publications

The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test

The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test

Discrete convolution statistic for hypothesis testing

Wald’s Method and Nikulin-Rao-Robson Test

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