• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.431-443
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• 2019

Goodness-of-fit techniques are an important topic in statistical analysis. Censored data occur frequently in survival experiments; therefore, many studies are conducted when data are censored. In this paper we mainly consider test statistics based on the empirical distribution function (EDF) to test normal distributions with unknown location and scale parameters when data are randomly censored. The most famous EDF test statistic is the Kolmogorov-Smirnov; in addition, the quadratic statistics such as the $Cram{\acute{e}}r-von$ Mises and the Anderson-Darling statistic are well known. The $Cram{\acute{e}}r-von$ Mises statistic is generalized to randomly censored cases by Koziol and Green (Biometrika, 63, 465-474, 1976). In this paper, we generalize the Anderson-Darling statistic to randomly censored data using the Kaplan-Meier estimator as it was done by Koziol and Green. A simulation study is conducted under a particular censorship model proposed by Koziol and Green. Through a simulation study, the generalized Anderson-Darling statistic shows the best power against almost all alternatives considered among the three EDF statistics we take into account.

• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.241-256
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• 2006

We generalize the $Cram{\acute{e}}r$-von Mises Statistic to test multivariate normality using Roy's union-intersection principle. We show the limit distribution of the suggested statistic is representable as the integral of a suitable Gaussian process. We also consider the computational aspects of the proposed statistic. Power performance is assessed in a Monte Carlo study.

• The Korean Journal of Applied Statistics
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• v.25 no.2
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• pp.311-319
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• 2012

The simplest and the most important distribution in survival analysis is exponential distribution. Koziol and Green (1976) derived Cram$\acute{e}$r-von Mises statistic's randomly censored version based on the Kaplan-Meier product limit estimate of the distribution function; however, it could not be practical for a real data set since the statistic is for testing a simple goodness of fit hypothesis. We generalized it to the composite hypothesis for exponentiality with an unknown scale parameter. We also considered the classical Kolmogorov-Smirnov statistic and generalized it by the exact same way. The two statistics are compared through a simulation study. As a result, we can see that the generalized Koziol-Green statistic has better power in most of the alternative distributions considered.

• 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.

• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.167-187
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• 2006

We introduce the concepts of intuitionistic fuzzy submodules and intuitionistic fuzzy weak congruences on an R-module (Near-ring module). And we obtain the correspondence between intuitionistic fuzzy weak congruences and intuitionistic fuzzy submodules of an R-module. Also, we define intuitionistic fuzzy quotient R-module of an R-module over an intuitionistic fuzzy submodule and obtain the correspondence between intuitionistic fuzzy weak congruences on an R-module and intuitionistic fuzzy weak congruences on intuitionistic fuzzy quotient R-module over an intuitionistic fuzzy submodule of an R-module.

• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.8
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• pp.883-888
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• 2014

Simulation is now using in various area as an effective decision analysis tool in complex environment of today. But, There is a focus to the simulation model development and execution better than result analysis. This article will emphasis to the importance of result analysis apart from model development in simulation, and will use R package for profit optimization simulation. R has a various function in statistic analysis and data manipulation, graphic display. So this research can show the value of R as a tool for simulation.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.973-981
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• 2021

Let R be a commutative ring with identity 1, n ≥ 3, and let 𝒯_n(R) be the linear Lie algebra of all upper triangular n × n matrices over R. A linear map 𝜑 on 𝒯_n(R) is called to be strong commutativity preserving if [𝜑(x), 𝜑(y)] = [x, y] for any x, y ∈ 𝒯_n(R). We show that an invertible linear map 𝜑 preserves strong commutativity on 𝒯_n(R) if and only if it is a composition of an idempotent scalar multiplication, an extremal inner automorphism and a linear map induced by a linear function on 𝒯_n(R).

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.155-166
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• 2018

Consider FARIMA time series with innovations that have infinite variances. We are interested in the estimation of self-similarities $H_n$ of FARIMA(0, d, 0) by using modified R/S statistic. We can confirm that the $H_n$ converges to Hurst parameter $H=d+\frac{1}{2}$. Finally, we figure out ARMA and minimum variance power spectrum density of FARIMA processes.

• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.155-162
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• 2017

In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination $R^2$ and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in $R^2$ and F-statistic.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.811-823
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• 2018

Multivariate control chart based on Hotelling's $T^2$ statistic is a powerful tool in statistical process control for identifying an out-of-control process. It is used to monitor multiple process characteristics simultaneously. Detection of the out-of-control signal with the $T^2$ chart indicates mean vector shifts. However, these multivariate signals make it difficult to interpret the cause of the out-of-control signal. In this paper, we review methods of signal interpretation based on the Mason, Young, and Tracy (MYT) decomposition of the $T^2$ statistic. We also provide an example on how to implement it using R software and demonstrate simulation studies for comparing the performance of these methods.