• 응용통계연구
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• 제24권6호
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• pp.1161-1168
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• 2011

The approximation for the distribution functions of nonparametric test statistics is a significant step in statistical inference. A rank sum test for dispersions proposed by Ansari and Bradley (1960), which is widely used to distinguish the variation between two populations, has been considered as one of the most popular nonparametric statistics. In this paper, the statistical tables for the distribution of the nonparametric Ansari-Bradley statistic is produced by use of polynomially adjusted normal approximation as a semi parametric density approximation technique. Polynomial adjustment can significantly improve approximation precision from normal approximation. The normal-polynomial density approximation for Ansari-Bradley statistic under finite sample sizes is utilized to provide the statistical table for various combination of its sample sizes. In order to find the optimal degree of polynomial adjustment of the proposed technique, the sum of squared probability mass function(PMF) difference between the exact distribution and its approximant is measured. It was observed that the approximation utilizing only two more moments of Ansari-Bradley statistic (in addition to the first two moments for normal approximation provide) more accurate approximations for various combinations of parameters. For instance, four degree polynomially adjusted normal approximant is about 117 times more accurate than normal approximation with respect to the sum of the squared PMF difference.

• Journal of the Korean Data and Information Science Society
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• 제11권2호
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• pp.139-155
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• 2000

An exclusive simulation study is conducted in computing means for order statistics in standard normal variate. Monte Carlo moments are used in Shapiro-Francia W' statistic computation. Finally, quantiles for Shapiro-Francia W' are generated. The study shows that in computing means for order statistics in standard normal variate, complicated distributions and intensive numerical integrations can be avoided by using Monte Carlo simulation. Lack of accuracy is minimal and computation simplicity is noteworthy.

• Communications for Statistical Applications and Methods
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• 제14권3호
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• pp.679-686
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• 2007

Moment expressions are derived for the internally truncated normal distributions commonly applied to screening and constrained problems. They are obtained from using a recursive relation between the moments of the normal distribution whose distribution is truncated in its internal part. Closed form formulae for the moments can be presented up to $N^{th}$ order under the internally truncated case. Necessary theories and two applications are provided.

• International Journal of Reliability and Applications
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• 제17권1호
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• pp.65-84
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• 2016

Motivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy exponentiated Frechet distribution (KEF). We derive some mathematical properties of the (KEF) including moment generating function, moments, quantile function and incomplete moment. We provide explicit expressions for the density function of the order statistics and their moments. In addition, the method of maximum likelihood and least squares and weighted least squares estimators are discuss for estimating the model parameters. A real data set is used to illustrate the importance and flexibility of the new distribution.

• Journal of the Korean Statistical Society
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• 제9권2호
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• pp.145-172
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• 1980

Draper and Lawrence (1965a) have given mixture designs for three factors when all the mixture components can vary on the entire factor space so that the region of interest is an equilateral triangle in two dimensions. In this paper their work is extended to the cases when the region of interest is an echelon, parallelogram, pentagon or hexagon, because of the restirctions imposed on some or all of the mixture components. The principles used in the choice of appropriate designs are those originally introduced by Box and Draper(1959). It is assumed that a response surface equation of first order is fitted, but there is a possibility of bias error due to presence of second order terms in the true model. Minimum bias designs for several cases of restricted regions of interest are illustrated.

• Communications for Statistical Applications and Methods
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• 제23권5호
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• pp.363-383
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• 2016

The Weibull family of lifetime distributions play a fundamental role in reliability engineering and life testing problems. This paper investigates the potential usefulness of transmuted new generalized Weibull (TNGW) distribution for modeling lifetime data. This distribution is an important competitive model that contains twenty-three lifetime distributions as special cases. We can obtain the TNGW distribution using the quadratic rank transmutation map (QRTM) technique. We derive the analytical shapes of the density and hazard functions for graphical illustrations. In addition, we explore some mathematical properties of the TNGW model including expressions for the quantile function, moments, entropies, mean deviation, Bonferroni and Lorenz curves and the moments of order statistics. The method of maximum likelihood is used to estimate the model parameters. Finally the applicability of the TNGW model is presented using nicotine in cigarettes data for illustration.

• Communications for Statistical Applications and Methods
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• 제23권2호
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• pp.147-161
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• 2016

This paper introduces the four parameter new generalized inverse Weibull distribution and investigates the potential usefulness of this model with application to reliability data from engineering studies. The new extended model has upside-down hazard rate function and provides an alternative to existing lifetime distributions. Various structural properties of the new distribution are derived that include explicit expressions for the moments, moment generating function, quantile function and the moments of order statistics. The estimation of model parameters are performed by the method of maximum likelihood and evaluate the performance of maximum likelihood estimation using simulation.

• International Journal of Reliability and Applications
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• 제4권4호
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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.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.603-613
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• 2005

We propose some estimators of the location parameter and derive the approximate maximum likelihood estimators (AMLEs) of the scale parameter in the exponential distribution based on multiply Type-II censored samples. We calculate the moments for the proposed estimators of the location parameter, and the AMLEs which are the linear functions of the order statistics. We compare the proposed estimators in the sense of the mean squared error (MSE) for various censored samples.

• 방송공학회논문지
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• 제19권2호
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• pp.195-204
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• 2014

이 논문에서는 순환정상 프로세스의 고차 통계 특성을 바탕으로 2-FSK, 4-FSK, 8-FSK, MSK, BPSK, QPSK, 8-PSK, 16-QAM, 32-QAM, 64-QAM 등 10개의 기저대역 디지털 변조신호를 자동으로 인식하는 방법을 제안하였다. 변조신호의 고유한 성질을 나타내는 특징변수로는 1차 순환 모멘트와 고차 순환 큐뮬런트를 이용하였다. 제안한 변조인식기는 크게 두 단계로 구성되며, 첫 번째 단계에서는 1차 순환 모멘트가 나타내는 첨두치를 이용하여 M-FSK와 비FSK로 변조신호를 분류한다. 두 번째 단계에서는 비FSK를 분류하기 위해 고차 순환 큐뮬런트 값을 이용하는 Gaussian 혼합 모델 기반의 분류기를 적용하였다. 제안한 방법의 성능을 검증하기 위해서 모의실험을 실시하였다. 모의실험 결과 제안한 분류기는 주파수와 위상 옵셋이 존재하는 환경에서도 우수한 분류확률을 나타내었다.