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

• International Journal of Reliability and Applications
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• v.9 no.1
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• pp.31-52
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• 2008

In this paper generalized version of the geometric distribution is introduced. This distribution can be considered as a two-parameter generalization of the discrete geometric distribution. The main statistical and reliability properties of this distribution are discussed. Two methods of estimation, namely maximum likelihood method and the method of moments are used to estimate the parameters of this distribution. Simulation is utilized to calculate these estimates and to study some of their properties. Also, asymptotic confidence limits are established for the maximum likelihood estimates. Finally, the appropriateness of this new distribution for a set of real data, compared with the geometric distribution, is shown by using the likelihood ratio test and the Kolmogorove-Smirnove test.

• International Journal of Reliability and Applications
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• v.2 no.4
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• pp.263-268
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• 2001

Shanmugam(1991) generalized the Poisson distribution to capture a restriction on the incidence rate $\theta$ (i.e. $\theta$ ＜ $\beta$, an unknown upper limit), and named it incidence rate restricted Poisson (IRRP) distribution. Using Neyman's C($\alpha$) concept, Shanmugam then devised a hypothesis testing procedure for $\beta$ when $\theta$ remains unknown nuisance parameter. Shanmugam's C ($\alpha$) based .results involve inverse moments which are not easy tools, This article presents an alternate testing procedure based on likelihood ratio concept. It turns out that likelihood ratio test statistic offers more power than the C($\alpha$) test statistic. Numerical examples are included.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37A no.11
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• pp.943-951
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• 2012

In this paper, we propose a novel spectrum sensing scheme based on the order statistic for cooperative cognitive radio network in non-Gaussian noise environments. Specifically, we model the ambient noise as the bivariate isotropic symmetric ${\alpha}$-stable random variable, and then, propose a cooperative spectrum sensing scheme based on the order of observations and the generalized likelihood ratio test. From numerical results, it is confirmed that the proposed scheme offers a substantial performance improvement over the conventional scheme in non-Gaussian noise environments.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.112-121
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• 1995

Let $p_1$ and $p_2$ be the proportions of two populations. To test the hypothesis $H_0 : p_1 = p_2$, we usually use the $x^2$ statistic, the large sample binomial statistic Z, and the Generalized Likelihood Ratio statistic-2log $\lambda$developed based on different mathematical rationale, respectively. Since testing the above hypothesis is equivalent to testing whether two populations follow the common Bernoulli distribution, one may also test the hypothesis by comparing 1 with the ratio of each density estimate and the hypothesized common density estimate, called comparison density, which was devised by Parzen(1988). We show that the above traditional test statistics ate actually estimating the measure of distance between the true densities and the common density under $H_0$ by representing them with the comparison density.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.543-557
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• 2006

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.

• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.455-467
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• 2003

There has been a long debate on the applicability of the chi-square approximation to statistics based on small sample size. Extending comparison results among Pearson chi-square Χ$^2$, generalized likelihood .ratio G$^2$, and the power divergence Ι(2/3) statistics suggested by Rudas(1986), recently developed disparity statistics (BWHD(1/9), BWCS(1/3), NED(4/3)) we compared and analyzed in this paper. By Monte Carlo studies about the independence model of two dimension contingency tables, the conditional model and one variable independence model of three dimensional tables, simulated 90 and 95 percentage points and approximate 95% confidence intervals for the true percentage points are obtained. It is found that the Χ$^2$, Ι(2/3), BWHD(1/9) test statistics have very similar behavior and there seem to be applcable for small sample sizes than others.

• The Korean Journal of Applied Statistics
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• v.10 no.1
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• pp.105-119
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• 1997

Barnwal and Paul(1988) derived the likelihood ratio statistic and $C(\alpha)$ statistic for testing the equality of the means of several groups of count data in the presence of a common dispersion parameter. These tests are generalized to be applicable without the restriction of a common dispersion parameter. And the assumed model of data is also extended from negative binomial to double exponential Poisson model. Monte Carlo simulations show the superiority of $C(\alpha)$ statistic based on the double exponential Poisson family which has a very simple form and requires estimates of the parameters only under the null hypothesis.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.11
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• pp.1545-1550
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• 2014

Fault detection and diagnosis (FDD) of photovoltaic (PV) power systems is one of significant techniques for reducing economic loss due to abnormality occurred in PV modules. This paper presents a new FDD method against PV power systems by using statistical comparison. This comparative approach includes deviation signals between the outputs of two neighboring PV modules. We first define a binary hypothesis testing under such deviation and make use of a generalized likelihood ratio testing (GLRT) theory to derive its FDD algorithm. Additionally, a recursive computational mechanism for our proposed FDD algorithm is presented for improving a computational effectiveness in practice. We carry out a real-time experiment to test reliability of the proposed FDD algorithm by utilizing a lab based PV test-bed system.

• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1661-1671
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• 2016

Risk analysis is a systematic study of uncertainties and risks we encounter in business, engineering, public policy, and many other areas. Value at Risk (VaR) is one of the most widely used risk measurements in risk management. In this paper, the Korean Composite Stock Price Index data has been utilized to model the VaR employing the classical ARMA (1,1)-GARCH (1,1) models with normal, t, generalized hyperbolic, and generalized pareto distributed errors. The aim of this paper is to compare the performance of each model in estimating the VaR. The performance of models were compared in terms of the number of VaR violations and Kupiec exceedance test. The GARCH-GPD likelihood ratio unconditional test statistic has been found to have the smallest value among the models.