• Communications for Statistical Applications and Methods
• /
• v.13 no.2
• /
• pp.297-307
• /
• 2006

Most methods for describing the relationship among random variables require specific probability distributions and some assumptions of random variables. The mutual information based on the entropy to measure the dependency among random variables does not need any specific assumptions. And the redundancy which is a analogous version of the mutual information was also proposed. In this paper, the redundancy and mutual information are explored to multi-dimensional categorical data. It is found that the redundancy for categorical data could be expressed as the function of the generalized likelihood ratio statistic under several kinds of independent log-linear models, so that the redundancy could also be used to analyze contingency tables. Whereas the generalized likelihood ratio statistic to test the goodness-of-fit of the log-linear models is sensitive to the sample size, the redundancy for categorical data does not depend on sample size but its cell probabilities itself.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.18 no.33
• /
• pp.93-102
• /
• 1995

In this study we are concerned with the diagnostics method of cross-classified categorical data using logistic regression model of binary response models for cell proportions. under this model, we could examine the goodness-of-fit of the models using Pearson's $x^2$test statistic and likelihood ratio statistic. Under this model, these statistics are assumed that sample survey schemes are with replacement sampling model. But these statistics are often inappropriate for analysing contingency tables consists of complex sampling schemes obtained sample survey data. In this study we are examined diagnostics procedures detecting any outlying cell proportions and influential observations on design space in logistic regression modeltake account of the survey design effects.

• Journal of Integrative Natural Science
• /
• v.5 no.3
• /
• pp.151-156
• /
• 2012

Because of the equivalence between control chart procedures and hypothesis testing, we propose to use likelihood ratio test (LRT) statistic $Z_i^2$ as the multivariate control statistic for simultaneous monitoring means of the multivariate normal process. Properties and comparisons of the proposed control charts are explored and conducted for matched fixed sampling interval (FSI) and variable sampling interval (VSI) with two sampling interval charts. The result of numerical comparisons shows that EWMA chart with two sampling interval procedure is more efficient than the corresponding FSI chart for small or moderate changes. When large shift of the process has occurred, we also found that Shewhart chart is more efficient than EWMA chart.

• International Journal of Reliability and Applications
• /
• v.1 no.2
• /
• pp.115-121
• /
• 2000

The trend change in aging properties, such as failure rate and mean residual life, of a life distribution is important to engineers and reliability analysts. In this paper we develop a test statistic for testing whether or not the failure rate changes its trend using censored data. The asymptotic normality of the test statistics is established. We discuss the efficiency values of loss due to censoring.

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.2
• /
• pp.187-199
• /
• 2003

We deal with the problem of testing a sequence of independent normal random variables with constant, known or unknown, variance for no change in mean versus alternatives with a single change-point. Various tests based on the likelihood ratio and recursive residuals, score statistics and cusums are studied. Proposed tests are modified version of Buckley's cusum statistics. A comparison study of various change-point test statistics is done by Monte Carlo simulation with S-plus software.

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.111-118
• /
• 2002

We study the influence of observations on testing a linear hypothesis using single and multiple case-deletions. The change in the F-test statistic due to case-deletions is shown to be completely determined by two externally Studentized residuals. These residuals we used for investigating the outlyingness when there are linear constraints or not. An illustrative example is given. It shows the usefulness of case-deletions.

• Journal of the Korean Statistical Society
• /
• v.23 no.1
• /
• pp.89-102
• /
• 1994

A new method for approximating the average run length (ARL) of cumulative sum (CUSUM) chart is proposed. This method uses the conditional expectation for the test statistic before the stopping time and its asymptotic conditional density function. The values obtained by this method are compared with some other methods in normal and exponential case.

• Communications for Statistical Applications and Methods
• /
• v.4 no.2
• /
• pp.435-444
• /
• 1997

The objective of this study is to investigate the problem of goodness of fit testing based on nonparametric function estimation techniques for the random censorship model. The small and large sample properties of the proposed test, $E_{mn}$, were investigated and it is shown that under the proportional hazard model $E_{mn}$ has higher power compared to the powers of the Kolmogorov -Smirnov, Kuiper, Cramer-von Mises, and analogue of the Cramer-von Mises type test statistic.

• Communications for Statistical Applications and Methods
• /
• v.11 no.2
• /
• pp.413-418
• /
• 2004

Statistically illiterate people seem to believe that there are some strategies for choosing winning numbers in lottery. One seemingly plausible strategy is to select the hot numbers which most frequently appeared in the past. In this article we investigate the existence of hot numbers in the Korean national lottery called Lotto. A numerical method is proposed to estimate the exact sampling distribution of test statistic for checking the existence of hot numbers among 45 possible numbers of choice.

• Communications for Statistical Applications and Methods
• /
• v.5 no.3
• /
• pp.935-944
• /
• 1998

This paper investigates the problem of goodness of fit tests for no effect model. The proposed test statistic $Z_{mn}$ is obtained by multiplying constant on the model free curve estimation techniques. The small and large sample properties of$Z_{mn}$ are investigated and the good results of power studies for the proposed test are illustrated.