• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.303-312
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• 2004

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter. This is the peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose non parametric maximum likelihood estimators of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.41-50
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• 1998

There are various notions of partial ordering between life-times of systems; stochastic ordering failure rate ordering and likeli-hood ration ordering. In this paper we show that for series systems with non i.i.d. exponential lifetimes of components standby redundancy at component level is better than that at system level in failure rate or-dering and likelihood ratio ordering. We also demonstrate that for 2-component parallel systems with i.i.d. exponential lifetimes of com-ponents standby system redundancy is better than standby component redundancy in failure rate ordering and likelihood ratio ordering.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.71-78
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• 2001

Three test statistics are proposed for the presence of seasonality in multiplicative seasonal time series models. Further their common limiting distribution is derived under some assumptions.

• Communications for Statistical Applications and Methods
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• v.31 no.1
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• pp.65-85
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• 2024

The tail probability of a function of a multivariate random variable is not easy to estimate by the crude Monte Carlo simulation. When the occurrence of the function value over a threshold is rare, the accurate estimation of the corresponding probability requires a huge number of samples. When the explicit form of the cumulative distribution function of each component of the variable is known, the inverse transform likelihood ratio method is directly applicable scheme to estimate the tail probability efficiently. The method is a type of the importance sampling and its efficiency depends on the selection of the importance sampling distribution. When the cumulative distribution of the multivariate random variable is represented by a copula and its marginal distributions, we develop an iterative algorithm to find the optimal importance sampling distribution, and show the convergence of the algorithm. The performance of the proposed scheme is compared with the crude Monte Carlo simulation numerically.

• International Journal of Reliability and Applications
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• v.15 no.1
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• pp.65-76
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• 2014

In this article, a new model based on Lomax distribution is introduced. This new model is both useful and practical in areas such as economic, reliability and life testing. Some statistical properties of this model are presented including moments, hazard rate, reversed hazard rate, mean residual life and mean inactivity time functions, among others. It is also shown that the distributions of the new model are ordered with respect to the strongest likelihood ratio ordering. The method of moment and maximum likelihood estimation are used to estimates the unknown parameters. Simulation is utilized to calculate the unknown shape parameter and to study its properties. Finally, to illustrate the concepts, the appropriateness of the new model for real data sets are included.

• 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.

• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.15-22
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• 2013

In clinical study or epidemic research, the $2{\times}2$ frequency table is useful to present a summary statistic The values of four cells in $2{\times}2$ table use to calculate the effect measures such as risk ratio, relative ris ratio or odds ratio. In this paper, we suggest that the improved visualization method using a radar diagram supported by MS-office Excel from the $2{\times}2$ frequency table is able to understand and draw easily betweendiagnosti measures such as sensitivity, specificity, predictivity, and likelihood ratio. We use some numerical example in order to show the usage of the proposed method.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.1-10
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• 2003

We consider obtaining graphical summaries of uncertainty in estimates of parameters in nonlinear models. A nonlinear constrained optimization algorithm is developed for likelihood based confidence intervals for the functions of parameters in the model The results are applied to the problem of finding significance levels in nonlinear models.

• Journal of the Korean Statistical Society
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• v.21 no.1
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• pp.14-26
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• 1992

In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing multisample sphericity have been derived in the null and nonnull cases when the alternatives are close to the null hypothesis. These expansions are obtained in the form of series of data distributions.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.347-355
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• 2001

We propose a method for detecting influential observations that have a large influence on the likelihood ratio test statistic for the two sets of variables are uncorrelated with one another. For this purpose we derive a local influence measure for the likelihood ratio test statistic under certain perturbation scheme. An illustrative example is given to show the effectiveness of the proposed method on the identification of influential observations.