• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.141-153
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• 2006

In this paper, we present the U-Statistic test for testing exponentiality against new renewal better than used (NRBU) based on a goodness of fit approach. Selected critical values are tabulated for sample sizes n=5(1)30(10)50. The asymptotic Pitman relative efficiency relative to (NRBU) test given in the work of Mahmoud et all (2003) is studied. The power estimates of this test for some commonly used life distributions in reliability are also calculated. Some of real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. The problem in case of right censored data is also handled.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.303-311
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• 2003

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts, et al.(2000) presented $T_1=\sum\limits_{i=1}^k(\hat{p}_i-p_i)^2$ as a test statistic with the local polynomial estimator $(\hat{p}_i$, and showed its asymptotic distribution. When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T=\sum\limits_{i=1}^k(\hat{p}_i-p_i)^2/p_i$ instead, and show it follows an asymptotic normal distribution.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.313-321
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• 2004

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts et al. (2000) presented T=${{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2$ as a test statistic with the local least square polynomial estimator ${{p}_{i}}^{*}$, and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood polynomial estimator ${{\hat{p}}_{i}}$, however, guarantees positive estimates for cell probabilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T_1={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of $T_2={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ where the minimum expected cell frequency is very small.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1057-1065
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• 2010

In this paper we discuss some cautionary notes in using the Pearson chi-squared test statistic for the goodness-of-fit of the ordinal response model. If a model includes continuous type explanatory variables, the resulting table from the t of a model is not a regular one in the sense that the cell boundaries are not fixed but randomly determined by some other criteria. The chi-squared statistic from this kind of table does not have a limiting chi-square distribution in general and we need to be very cautious of the use of a chi-squared type goodness-of-t test. We also study the limiting distribution of the chi-squared type statistic for testing the goodness-of-t of cumulative logit models with ordinal responses. The regularity conditions necessary to the limiting distribution will be reformulated in the framework of the cumulative logit model by modifying those of Moore and Spruill (1975). Due to the complex limiting distribution, a parametric bootstrap testing procedure is a good alternative and we explained the suggested method through a practical example of an ordinal response dataset.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.623-632
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• 2007

Some tests of the goodness of fit of the uniform distribution between 0 and 1 are presented. The powers of the tests under certain alternatives are examined. As a result, the statistic based on the difference between the order statistics and the modal value of them gives good powers. We also give modifications of the statistic without using the extensive tables of the critical points.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.489-498
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• 1998

The influence of observations the on the goodness-of-fit test in maximum likelihood factor analysis is investigated by using the local influence method. under an appropriate perturbation the test statistic forms a surface. One of main diagnostics is the maximum slope of the perturbed surface the other is the direction vector cor-responding to the curvature. These influence measures provide the information about jointly influence measures provide the information about jointly influential observations as well as individ-ually influential observations.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.519-527
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• 2004

Relationship between the partial likelihood ratio statistics for logisitic models and the partial goodness-of-fit statistics for corresponding log-linear models is discussed. This paper shows how definitions of suppression in logistic model can be adapted for log-linear model and how they are related to confounding in terms of collapsibility for categorical data. Several $2{times}2{times}2$ contingency tables are illustrated.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• Journal of the Korean Data and Information Science Society
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• v.13 no.1
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• pp.113-119
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• 2002

A powerful and easily computed goodness-of-fit test for Pareto distribution which does not depend on the unknown location and scale parameters is proposed based on the transformed sample Lorenz curve. We compare the power of the proposed test statistic with the other goodness-of-fit tests for Pareto distribution against various alternatives through Monte Carlo methods.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.277-284
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• 2000

The transformed sample Lorenz curve provides a powerful and easily computed goodness-of-fit test for exponentiality which does not depend on the unknown scale parameter. We compare the power of the transformed sample Lorenz curve statistic with the other goodness-of-fit tests for exponentiality against various alternatives through Monte Carlo methods and discuss the results.