• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.487-495
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• 2010

This paper develops a goodness of fit test statistic to test if the progressively Type II censored sample comes from an exponential distribution with origin known. The test is based on normalizing spacings and Stephens (1978)' modified Shapiro and Wilk (1972) test for exponentiality. The modification is for the case where the origin is known. We applied the same modification to Kim (2001a)'s statistic, which is based on the ratio of two asymptotically efficient estimates of scale. The simulation results show that Kim (2001a)'s statistic has higher power than Stephens' modified Shapiro and Wilk statistic for almost all cases.

• The Korean Journal of Applied Statistics
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• v.17 no.1
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• pp.35-47
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• 2004

In this paper, we generalizes Kim and Bickel(2003)'s statistic for bivariate normality to that of multinormality, applying Fattorini(1986)'s method. Fattorini(1986) generalized Shapiro-Wilk's statistic for univariate normality to multivariate cases. The proposed statistic could be considered as an approximate statistic to Fattorini(1986)'s. It can be used even for a big sample size. Power performance of the proposed test is assessed in a Monte Carlo study.

• The Korean Journal of Applied Statistics
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• v.21 no.2
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• pp.265-273
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• 2008

Kim (2001a) presented a modification of the Shapiro and Wilk (1972) test for exponentiality based on the ratio of two asymptotically efficient estimates of scale. In this paper we modify this test statistic when the sample is censored. We use the normalized spacings based on the sample data, which was used in Samanta and Schwarz (1988) to modify the Shapiro and Wilk (1972) statistic to the censored data. As a result the modified statistics have the same null distribution as the uncensored case with a corresponding reduction in sample size. Through a simulation study it is found that the proposed statistic has higher power than Samanta and Schwarz (1988) statistic especially for the alternatives with the coefficient of variation greater than or equal to 1.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.583-590
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• 2008

In this article, we focuss on. sequences of polynomials with {$\pm1$} coefficients constructed by recursive argument that is known as Rudin-Shapiro polynomials. The asymptotic behavior of these polynomials defines as the ratio of their 2q-norm with 2-norm to be dominated by some number depending on q or "the best" by an absolute constant. In this work we first show the conjecture holds for some finite numbers of m and then introduce a technique that give the result for any positive odd integer m whenever it holds for all pervious even numbers.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.243-248
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• 2003

Fattorini(1986)의 통계량은 Shapiro와 Wilk의 일변량 정규분포를 위한 검정통계량을 다변량으로 확장한 것이다. 본 논문에서는 Kim과 Bickel(2003)에서 제안한 이변량 정규분포를 위한 검정통계량을 Fattorini(1986)의 방법을 이용하여 이변량 이상인 경우에도 실제적으로 사용가능하도록 일반화하였다. 제안된 통계량은 Fattorini(1986) 통계량의 근사통계량으로 생각할 수 있으며 표본의 크기가 클 때도 사용가능하다.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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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.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.1-10
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• 1999

Table of the empirical quantiles for the well known Shapiro-Francia W' goodness of fit statistic is produced which is more accurate than the existing ones. Prediction equation for the quantiles of W' statistic for sample sizes 30 or more we developed. The process of computing the expected values for the standard normal variate is discussed. This work is intended to make the Shapiro-Francia W' statistic more accessible to the practitioner.

• Bulletin of the Korean Chemical Society
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• v.13 no.2
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• pp.192-199
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• 1992

A modified Shapiro reaction was developed using N,N-diethylaminosulfonylhydrazones.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.5
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• pp.418-428
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• 2007

In the calculation of wave propagation by Boussinesq equation model, it is very common to experience numerical noises generated from nonlinear interaction and breaking wave occurrence, and the numerical solution is rapidly diverged unless the noises are properly controlled. A comparative study was here undertaken for the characteristics of three different lowpass filters (FFT filter, Gaussian filter and Shapiro filter) which are all designed to be applied to the interim results of numerical calculation. The numerical results obtained with application of respective filter techniques were compared with the results of an existing hydraulic experiment for the aspects of noise suppression, conservation of main signal and altering time. The results show that the Shapiro filter can be best applied with optimal choices of its element number, pass number and filtering tune interval. The combination of the number of filter element off, pass number of 50 or less, and application interval of 100 to 200 time steps generally showed good performance in both accuracy and efficiency of the numerical calculation.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.973-981
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• 2008

In this paper we focus on a type of Unimodular polynomial pair used for digital systems and present some new properties of them which lead us to estimation of their autocorrelation coefficients and the moments of a Rudin-Shapiro polynomial product. Some new results on the Rudin-shapiro sequences will be presented in the last section. Main Facts: For positive integers M and n with $M\;<\;2^n$ - 1, consider the $2^n$ - M numbers ${\epsilon}_k$ ($M\;{\leq}\;k\;{\leq}\;2^n$ - 1) which form a collection of Rudin-Shapiro coefficients. We verify that $|{\sum}_{k=M}^{2^{n-1}}\;{{\epsilon}_k}e^{ikt}|$ is dominated by $(2+\sqrt{2})\;\sqrt {2^n-M}-{\sqrt{2}}$.