• Journal of the Korean Statistical Society
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• v.1 no.1
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• pp.11-17
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• 1973

A class of sequential binomial tests and a sequential rank test can be applied for testing two treatments when subjects are paired in many-to-one ratio. The efficiency of each test is examined in terms of the average sample number. The binomial tests are much easier and more convenient to apply than the rank test not as efficient. Within the class of binomial test, the median test appears to be the most efficient is general.

• Food Science and Biotechnology
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• v.15 no.4
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• pp.494-498
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• 2006

An increase in variance (overdispersion) can occur when a binomial statistical analysis is applied to sensory difference test data in which replicate sensory evaluations (tastings) and multiple evaluators (judges) are combined to increase the sample size. Such a practice can cause extensive Type I errors, leading to serious misinterpretations of the data, especially when traditional simple binomial analysis is applied. Alternatively, the use of beta binomial analysis will circumvent the problem of overdispersion. This brief review discusses the uses and computation methodology of beta binomial analysis and in practice evidence for the occurrence of overdispersion.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.33-36
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• 2008

We introduce some properties for fuzzy binomial distributions with fuzzy valued probability. First we define fuzzy type I error and type II error for fuzzy relative frequency and agreement index. And we show that an fuzzy power function and fuzzy binomial frequency function for binomial proportion test.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.433-444
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• 2016

When we observe binary responses in a cluster (such as rat lab-subjects), they are usually correlated to each other. In clustered binomial counts, the independence assumption is violated and we encounter an extra-variation. In the presence of extra-variation, the ordinary statistical analyses of binomial data are inappropriate to apply. In testing the homogeneity of proportions between several treatment groups, the classical Pearson chi-squared test has a severe flaw in the control of Type I error rates. We focus on modifying the chi-squared statistic by incorporating variance inflation factors. We suggest a method to adjust data in terms of dispersion estimate based on a quasi-likelihood model. We explain the testing procedure via an illustrative example as well as compare the performance of a modified chi-squared test with competitive statistics through a Monte Carlo study.

• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.829-843
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• 2010

To test for the serial dependence in time series of counts data, Jung and Tremayne (2003) evaluated the size and power of several tests under the class of INARMA models based on binomial thinning operations for Poisson marginal distributions. The overdispersion phenomenon(i.e., a variance greater than the expectation) is common in the real world. Overdispersed count data can be modeled by using alternative thinning operations such as random coefficient thinning, iterated thinning, and quasi-binomial thinning. Such thinning operations can lead to time series models of counts with negative binomial or generalized Poisson marginal distributions. This paper examines whether the test statistics used by Jung and Tremayne (2003) on serial dependence in time series of counts data are affected by overdispersion.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.2
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• pp.98-105
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• 2012

This paper describes the Bayesian approach for reliability demonstration test based on the samples from a finite population. The Bayesian approach involves the technical method about how to combine the prior distribution and the likelihood function to produce the posterior distribution. In this paper, the hypergeometric distribution is adopted as a likelihood function for a finite population. The conjugacy of the beta-binomial distribution and the hypergeometric distribution is shown and is used to make a decision about whether to accept or reject the finite population judging from a viewpoint of faulty goods. A numerical example is also given.

• Journal of the Korean Statistical Society
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• v.11 no.2
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• pp.131-138
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• 1982

Analogous to Singh's (1978) characterization of positive-Poisson distributioin and Shanmugam and Singh's (1992) characterization of logarithmic series distribution, a characterization and its statistical application of the negative binomial distribution truncated at zero are given in this paper. While it is known that under certain conditions the negative binomial distribution truncted at zero approaches the positive-Poisson and the logarithmic series distributions, we show here that the results of this paper approach in limit the results of Singh, and Shanmugam and Singh, respectively. Using the biologicla data from Sampford (1955), we illusrate our results. Also, expressions are explicitly given to test the hypothesis whether a random sample is indeed from a geometric distribution.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.511-518
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• 2009

We consider the problem of testing for change and estimating the unknown change-point in a sequence of time-ordered observations from the binomial and Poisson distributions. Including the likelihood ratio test, Gombay and Horvath (1990) tests are studied and the proposed change-point estimator is derived from their test statistic. A power study of tests and a comparison study of change-point estimators are done via simulation.

• The Korean Journal of Applied Statistics
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• v.21 no.2
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• pp.341-353
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• 2008

The bootstrap method for the score test statistic is proposed in a bivariate negative binomial distribution. The Monte Carlo study shows that the score test for testing overdispersion underestimates the nominal significance level, while the score test for "intrinsic correlation" overestimates the nominal one. To overcome this problem, we propose a bootstrap method for the score test. We find that bootstrap methods keep the significance level close to the nominal significance level for testing the hypothesis. An empirical example is provided to illustrate the results.

• The Korean Journal of Applied Statistics
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• v.23 no.4
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• pp.777-781
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• 2010

Yates' continuity correction of the chi-squared test for testing the homogeneity of two binomial proportions in $2{\times}2$ contingency tables is developed to lower the value of the test statistic slightly. The effect of continuity correction is expected to decrease as the sample size increases. However, in extremely unbalanced $2{\times}2$ contingency tables, we find some cases where the effect of continuity correction is eccentric and is larger than expected. In such cases, we conclude that the chi-squared test with continuity correction should not be employed as a test statistic in both asymptotic tests and exact tests.