• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.493-504
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• 2017

We often observe count data that exhibit over-dispersion, originating from too many zeros, and under-dispersion, originating from too few zeros. To handle this types of problems, the zero-altered distribution model is designed by Ghosh and Kim in 2007. Their model can control both over-dispersion and under-dispersion with a single parameter, which had been impossible ever. The dispersion type depends on the sign of the parameter ${\delta}$ in zero-altered distribution. In this study, we demonstrate the role of the dispersion type parameter ${\delta}$ through the data of the number of births in Korea. Employing both the chi-square statistic and the Kolmogorov statistic for goodness-of-fit, we also explained any difference between the theoretical distribution and the observed one that exhibits either over-dispersion or under-dispersion. Finally this study shows whether the test statistics for goodness-of-fit show any similarity with the role of the dispersion type parameter ${\delta}$ or not.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.507-516
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• 2011

Comparative studies on generalized binomial models (Moon, 2003; Ng, 1989; Paul, 1985; Kupper and Haseman, 1978; Griffiths, 1973) are restrictive in that the models compared are rather limited and MSE of the estimates is the only measure considered for the model adequacy. This paper is aimed to report simulation results which provide possible guidelines for selecting a proper model. We examine Pearson type of goodness-of-fit statistic to its degrees of freedom and AIC for the overall model quality. MSE and Bias of the individual estimates are also considered as the component fit measures. Performance of some models varies widely for a certain range of the parameter space while most of the models are quite competent. Our evaluation shows that the Extended Beta-Binomial model (Prentice, 1986) turns out to be particularly favorable in the point that it provides consistently excellent fit almost all over the values of the intra-class correlation coefficient and the probability of success.

• The Korean Journal of Applied Statistics
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• v.26 no.4
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• pp.611-622
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• 2013

Mudholkar and Tian (2002) proposed an entropy-based test of fit for the inverse Gaussian distribution; however, the test can be applied to only the composite hypothesis of the inverse Gaussian distribution with an unknown location parameter. In this paper, we propose an entropy-based goodness-of-fit test for an inverse Gaussian distribution that can be applied to the composite hypothesis of the inverse Gaussian distribution as well as the simple hypothesis of the inverse Gaussian distribution with a specified location parameter. The proposed test is based on the probability integration transformation. The critical values of the test statistic estimated by simulations are presented in a tabular form. A simulation study is performed to compare the proposed test under some selected alternatives with Mudholkar and Tian (2002)'s test in terms of power. The results show that the proposed test has better power than the previous entropy-based test.

• Journal of Korean Society for Quality Management
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• v.46 no.1
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• pp.95-112
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• 2018

Purpose: To find out the appropriate probability distribution of credit card usage behavior by considering the relationship among income, expenditure and credit card usage amount. Such relationship is enabled by Korea's especially high penetration of credit card. Method: Goodness-of-fit test and effect size statistic W were used to identify the distribution of income and credit card usage amount. A simulation model is introduced to generate the credit card transactions on individual user level. Result: The three data sets for testing had either passed the chi-square test or showed low W values, meaning they follow the exponential distribution. And the exponential distribution turned out to fit the data sets well. The r values were very high. Conclusion: The credit card usage behavior, denoted as the counts of users by usage amount band, follows the exponential distribution. This distribution is easy to manipulate, has a variety of applications and generates important business implications.

• Journal of Korean Society of Transportation
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• v.17 no.5
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• pp.99-110
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• 1999

This study deals with the adaptability questions of O-D table estimation models. Its objectives are two-fold; (1) to estimate the characteristics of various O-D table estimation models(i.e. linear regression models. entropy models and statistic models) and (2) to find the model which estimates the O-D table with the best accuracy under the various data conditions. In Pursuing the above, this study gives the particular attentions to the test of the models, using the Sioux Falls network and equilibrium assignment method of MINUTP. The major findings are the followings. Firstly. it finds that the statistic models have the most goodness of fat among all models, if the required data are all Prepared. But it Presents that statistic models are the most sensitive against the underspecification and inconsistency problems of link data. Secondly, It shows that the linear regression models have the worst goodness of fat among all models. But the linear regression models are the most insensitive to the underspecification and inconsistency problems. Thirdly, THE/1 model of entropy model is sensitive against the underspecification and incon-sistency problems, but THE/2 model is insensitive. Finally, other informations like total volume, zonal Production and attraction volumes in 0-D table, help models to gain the better goodness of fit. Especially, in the statistic models. both the zonal production and attraction volume data are helpful to estimate the link volumes. It can be expected that the results dive some implications not only to the selection of optimal model under the various given data, but also to the development or modification of model.

• Human Ecology Research
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• v.58 no.2
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• pp.149-161
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• 2020

This study showed that the association between grandmother-mother relationship and grandmother-grandchildren ties is mediated by the coparenting. Participants consisted of 329 grandmothers who were rearing preschool aged grandchildren in the Seoul and Gyeonggido area. SPSS 23.0 performed descriptive statistical analysis and correlation analysis. The structural equation model was estimated with AMOS 23.0. Parameters were estimated using the maximum likelihood method. Model fit index used the chi-square statistic, the goodness of fit index (GFI), the Turker-Lewis index (TLI), the comparative fit index (CFI), the root mean square error of approximation (RMSEA). The mediation effect analysis followed a two-step verification process; direct and indirect effect. In addition, statistical significance of the indirect effect was examined using a bootstrapping procedure. The results are as follows. First, a positive correlation was found between the grandmother-mother relationship, grandmother-grandchildren ties, and coparenting. Second, the association between grandmother-mother relationship and grandmother-grandchildren ties is mediated by coparenting. The results of this study suggest that the quality of the grandmother's relationship with mothers and cooperative coparenting is important to building relationships with grandchildren. In addition, coparenting can be an important mechanism for grandmother-mother relationships and grandmother-grandchild ties. Based on the results of this study, we discussed ways to improve the grandmothers' relationship quality with the mother and strengthen parenting ability.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.883-891
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• 2011

For survival data we sometimes want to test a log normality hypothesis that can be changed into normality by transforming the survival data. Hence the Shapiro-Wilk type statistic for normality is generalized to randomly censored data based on the Kaplan-Meier product limit estimate of the distribution function. Koziol and Green (1976) derived Cram$\acute{e}$r-von Mises statistic's randomly censored version under the simpl hypothesis. These two test statistics are compared through a simulation study. As for the distribution of censoring variables, we consider Koziol and Green (1976)'s model and other similar models. Through the simulation results, we can see that the power of the proposed statistic is higher than that of Koziol-Green statistic and that the proportion of the censored observations (rather than the distribution of censoring variables) has a strong influence on the power of the proposed statistic.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.473-495
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• 2019

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. A modified goodness-of-fit test using the Nikulin-Rao-Robson statistic test is investigated via two examples and is observed that the new extension might be used as an alternative lifetime model.

• International Journal of Reliability and Applications
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• v.14 no.1
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• pp.27-39
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• 2013

In this article, a new model based on the Rayleigh distribution is introduced. This model is useful and practical in physics, reliability, and life testing. The statistical and reliability properties of this model are presented, including moments, the hazard rate, the reversed hazard rate, and mean residual life functions, among others. In addition, it is shown that the distributions of the new model are ordered regarding the strongest likelihood ratio ordering. Four estimating methods, namely, method of moment, maximum likelihood method, Bayes estimation, and uniformly minimum variance unbiased, are used to estimate the parameters of this model. Simulation is used to calculate the estimates and to study their properties. Finally, the appropriateness of this model for real data sets is shown by using the chi-square goodness of fit test and the Kolmogorov-Smirnov statistic.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.159-171
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent ; that is, the power of the test will not approach 1 as the sample size increases. Hence we give a test based on the ratio of two asymptotically efficient estimates of scale. We also have conducted a power study to compare the test procedures, using Monte Carlo samples from a wide range of alternatives. It is found that the suggested statistics have higher power for the alternatives with the coefficient of variation greater that or equal to 1.