• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.313-320
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• 2015

In this research, we compare the efficiency of two test procedures proposed by Prentice and Gloeckler (1978) and Park and Hong (2009) for grouped data with possible right censored observations. Both test statistics were derived using the likelihood ratio principle, but under different semi-parametric models. We review the two statistics with asymptotic normality and consider obtaining empirical powers through a simulation study. The simulation study considers two types of models the location translation model and the scale model. We discuss some interesting features related to the grouped data and obtain null distribution functions with a re-sampling method. Finally we indicate topics for future research.

• International Journal of Reliability and Applications
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• v.2 no.2
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• pp.81-97
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• 2001

Lifetesting problems have been the subject of investigations for over three decades. Most suggested approaches are markedly different from those used in the related but wider goodness of fit problems. In the current investigation, it is demonstrated that a goodness of fit approach is possible in many lifetesting problems and that It results in simpler procedures that are asymptotically equivalent or better than standard ones. They may also have superior finite sample behavior. Several perennial classes are addressed here. The class of increasing failure rate (IFR) and the class of new better than used (NBU) are addressed first. In addition, we provide testing for a newer and practical class of new better than used in convex ordering (NBUC) due to Cao and Wang (1991). Other classes can be developed similarly and this point is illustrated with the classes of new better than used in expectation (NBUE) and harmonic new better than used in expectation (HNBUE).

• International Journal of Reliability and Applications
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• v.4 no.4
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• pp.191-199
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• 2003

In the present work, a moment inequality is derived for new renewal better (worse) than used in expectation(NRBUE) (NRWUE) distributions. This inequality demonstrates that if the mean life is finite then all higher order moments exist. A new test statistics for testing exponentiality against NRBUE (NRWUE) is introduced based on this inequality. It is shown that the proposed test is simple and has high relative efficiency for some commonly used alternatives. Critical values are tabulated for sample sizes n = 5(1)30. A set of real data is used as an example to elucidate the use of the proposed test statistics for practical reliability analysis.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.143-152
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• 1997

In this paper, we obtain maximum likelihood estimators for $P(X_{1}\;<\;X_{2})$ in the Marshall and Olkin's bivariate exponential model with bivariate censored data. The asymptotic normality of the estimator is derived. Also we propose approximate testing for $P(X_{1}\;<\;X_{2})$ based on the M.L.E. We compare the test powers under vsrious conditions through Monte Carlo simulation.

• Journal of Applied Reliability
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• v.18 no.3
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• pp.220-228
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• 2018

Purpose: The purpose of this study is to investigate the tail behavior of the life distribution which exhibits an increasing failure rate or other positive aging effects after a certain time point. Methods: We characterize the tail behavior of the life distribution with regard to certain reliability measures such as failure rate, mean residual life and reliability function and derive several stochastic properties regarding such life distributions. Also, utilizing an L-statistic and its asymptotic normality, we propose new nonparametric testing procedures which verify if the life distribution has an increasing tail failure rate. Results: We propose the IFR-Tail (Increasing Failure Rate in Tail), DMRL-Tail (Decreasing Mean Residual Life in Tail) and NBU-Tail (New Better than Used in Tail) classes, all of which represent the tail behavior of the life distribution. And we discuss some stochastic properties of these proposed classes. Also, we develop a new nonparametric test procedure for detecting the IFR-Tail class and discuss its relative efficiency to explore the power of the test. Conclusion: The results of our research could be utilized in the study of wide range of applications including the maintenance and warranty policy of the second-hand system.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.449-461
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• 2009

Higher sigma quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The process capability indices and the sigma level $Z_{st}$ ave been widely used in six sigma industries to assess process performance. Most evaluations on process capability indices focus on statistical estimation under normal process which may result in unreliable assessments of process performance. In this paper, we consider statistical estimation for bivariate VPCI(Vector-valued Process Capability Index) $C_{pkl}=(C_{pklx},\;C_{pklx})$ under Marshall and Olkin (1967)'s bivariate exponential process. First, we derive some limiting distribution for statistical inference of bivariate VPCI $C_{pkl}$. And we propose two asymptotic normal confidence regions for bivariate VPCI $C_{pkl}$. The proposed method may be very useful under bivariate exponential process. A numerical result based on our proposed method shows to be more reliable.

• Journal of Korea Water Resources Association
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• v.39 no.12 s.173
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• pp.997-1012
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• 2006

We have presented a nonparametric stochastic approach for the SOI(Southern Oscillation Index) series that used nonlinear methodology called Nonlinear AutoRegressive(NAR) based on conditional kernel density function and CAFPE(Corrected Asymptotic Final Prediction Error) lag selection. The fitted linear AR model represents heteroscedasticity, and besides, a BDS(Brock - Dechert - Sheinkman) statistics is rejected. Hence, we applied NAR model to the SOI series. We can identify the lags 1, 2 and 4 are appropriate one, and estimated conditional mean function. There is no autocorrelation of residuals in the Portmanteau Test. However, the null hypothesis of normality and no heteroscedasticity is rejected in the Jarque-Bera Test and ARCH-LM Test, respectively. Moreover, the lag selection for conditional standard deviation function with CAFPE provides lags 3, 8 and 9. As the results of conditional standard deviation analysis, all I.I.D assumptions of the residuals are accepted. Particularly, the BDS statistics is accepted at the 95% and 99% significance level. Finally, we split the SOI set into a sample for estimating themodel and a sample for out-of-sample prediction, that is, we conduct the one-step ahead forecasts for the last 97 values (15%). The NAR model shows a MSEP of 0.5464 that is 7% lower than those of the linear model. Hence, the relevance of the NAR model may be proved in these results, and the nonparametric NAR model is encouraging rather than a linear one to reflect the nonlinearity of SOI series.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.97-110
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• 2006

Since it is well-established that even high quality data tend to contain outliers, one would expect fat? greater reliance on robust regression techniques than is actually observed. But most of all robust regression estimators suffers from the computational difficulties and the lower efficiency than the least squares under the normal error model. The weighted self-tuning estimator (WSTE) recently suggested by Lee (2004) has no more computational difficulty and it has the asymptotic normality and the high break-down point simultaneously. Although it has better properties than the other robust estimators, WSTE does not have full efficiency under the normal error model through the weighted least squares which is widely used. This paper introduces a new approach as called the reweighted WSTE (RWSTE), whose scale estimator is adaptively estimated by the self-tuning constant. A Monte Carlo study shows that new approach has better behavior than the general weighted least squares method under the normal model and the large data.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.431-440
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• 2013

We consider the problem of estimating the parameters of heavy tailed distributions. In general, maximum likelihood estimation(MLE) is the most preferred method of parameter estimation because it has good properties such as asymptotic consistency, normality and efficiency. However, MLE is not always the best solution because MLE is unstable or does not exist in some cases. This paper proposes another parameter estimation method, non-linear least squares(NLS) and compares its performance to MLE. The NLS estimator is achieved by minimizing sum of squared difference between empirical cumulative distribution function(CDF) and a theoretical distribution function. In this article, we compare the NLS method to MLE using simulated data from heavy tailed distributions. The NLS method is shown to perform better than MLE in Burr distribution when the sample size is small; in addition, it performs well in a Frechet distribution.

• KDI Journal of Economic Policy
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• v.13 no.4
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• pp.117-140
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• 1991

The purpose of this paper is primarily to introduce a nonparametric statistical tool developed by Baek and Brock to detect a unidirectional causal ordering between two economic variables and apply it to interesting macroeconomic relationships among money, production and prices. It can be applied to any other causal structure, for instance, defense spending and economic performance, stock market index and market interest rates etc. A key building block of the test for nonlinear Granger causality used in this paper is the correlation. The main emphasis is put on nonlinear causal structure rather than a linear one because the conventional F-test provides high power against the linear causal relationship. Based on asymptotic normality of our test statistic, the nonlinear causality test is finally derived. Size of the test is reported for some parameters. When it is applied to a money, production and prices model, some evidences of nonlinear causality are found by the corrected size of the test. For instance, nonlinear causal relationships between production and prices are demonstrated in both directions, however, these results were ignored by the conventional F-test. A similar results between money and prices are obtained at high lag variables.