Chi-Square Test for Continuous Distributions with Shift and Scale Parameters

Nikulin, Mikhaïl

doi:10.1137/1118069

Cited by 77 publications

(55 citation statements)

References 3 publications

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“…However, it is well known that most of these tests are not asymptotically distribution free. This is true even for the chi-square type of tests with the exception of the modified chi-square statistic studied in Nikulin (1973) in the context of empirical processes. It is also well documented in the literature that chi-square type tests often have relatively low power against many alternatives of interest, see, for example, Moore (1986).…”

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confidence: 99%

Martingale transforms goodness-of-fit tests in regression models

Khmaladze

Koul

2004

Ann. Statist.

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This paper discusses two goodness-of-fit testing problems. The first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model, while the second pertains to fitting a parametric regression model when the error distribution is unknown. For the first problem the paper contains tests based on a certain martingale type transform of residual empirical processes. The advantage of this transform is that the corresponding tests are asymptotically distribution free. For the second problem the proposed asymptotically distribution free tests are based on innovation martingale transforms. A Monte Carlo study shows that the simulated level of the proposed tests is close to the asymptotic level for moderate sample sizes

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confidence: 99%

Martingale transforms goodness-of-fit tests in regression models

Khmaladze

Koul

2004

Ann. Statist.

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“…The well-known NRR statistic (Y 2 n ( Θ n )) is one of famous modified classical chi-squared goodness-offit test (GOF) that was introduced by Nikulin [7] and Rao and Robson [8]. This statistic test is based on the differences between theoretical and empirical probabilities to fall into grouping cells.…”

Section: Nrr Statistic Tes For Complete Datamentioning

confidence: 99%

A new class of distributions based on the zero truncated Poisson distribution with properties and applications

Abouelmagd¹,

Hamed²,

Handique³

et al. 2018

J. Nonlinear Sci. Appl.

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We study a new family of distributions defined by the minimum of the Poisson random number of independent and identically distributed random variables having the Topp Leone-G distribution. Some mathematical properties of the new family are derived. Maximum likelihood estimation of the model parameters is investigated. Two special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of the proposed family. In order to test the validity of the new family, a modified Chi-squared goodness-of-fit test based on Nikulin-Rao-Robson statistics is proposed theoretically.

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“…(i) Using ideas of Nikulin (1973), we consider recent modifications of Pearson's test for the Poisson and binomial distributions that are derived in the . The data of Table 2 are summarized in Table 3.…”

Section: A Statistical Analysis Of the Datamentioning

confidence: 99%

Poisson Versus Binomial: Appointment of Judges to the U.S. Supreme Court

Voinov¹,

Воинов²,

Rakhimova

2010

Aus NZ J of Statistics

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The problem of discriminating between the Poisson and binomial models is discussed in the context of a detailed statistical analysis of the number of appointments of the U.S. Supreme Court justices from 1789 to 2004. Various new and existing tests are examined. The analysis shows that both simple Poisson and simple binomial models are equally appropriate for describing the data. No firm statistical evidence in favour of an exponential Poisson regression model was found. Two attendant results were obtained by simulation: firstly, that the likelihood ratio test is the most powerful of those considered when testing for the Poisson versus binomial and, secondly, that the classical variance test with an upper-tail critical region is biased.

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Chi-Square Test for Continuous Distributions with Shift and Scale Parameters

Cited by 77 publications

References 3 publications

Martingale transforms goodness-of-fit tests in regression models

Martingale transforms goodness-of-fit tests in regression models

A new class of distributions based on the zero truncated Poisson distribution with properties and applications

Poisson Versus Binomial: Appointment of Judges to the U.S. Supreme Court

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