• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.629-637
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• 2002

Shapiro and Wilk(1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test based on the statistic is inconsistent Kim(2001a) proposed a modified Shapiro-Wilk's test statistic using the ratio of two asymptotically efficient estimators of scale. In this paper, we study the consistency of the proposed test.

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.473-481
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent. Kim(2001) proposed a modified Shapiro-Wilk's test statistic based on the ratio of tow asymptotically efficient estimates of scale. In this paper, we study the asymptotic behavior of the statistic using the approximation of the quantile process by a sequence of Brownian bridges and represent the limit null distribution as an integral of a Brownian bridge.

• International Journal of Reliability and Applications
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• 제16권2호
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• pp.123-133
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• 2015

In this paper, the problem of testing exponentiality against net decreasing variance residual lifetime (NDVRL) classes of life distributions is investigated. For this property a nonparametric test is presented based on kernel method. The test is presented for complete and right censored data. Furthermore, Pitman's asymptotic relative efficiency (PARE) is discussed to assess the performance of the test with respect to other tests. Selected critical values are tabulated. Some numerical simulations on the power estimates are presented for proposed test. Finally, numerical examples are presented for the purpose of illustrating our test.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.159-171
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent ; that is, the power of the test will not approach 1 as the sample size increases. Hence we give a test based on the ratio of two asymptotically efficient estimates of scale. We also have conducted a power study to compare the test procedures, using Monte Carlo samples from a wide range of alternatives. It is found that the suggested statistics have higher power for the alternatives with the coefficient of variation greater that or equal to 1.

• International Journal of Reliability and Applications
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• 제13권2호
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• pp.57-69
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• 2012

Our goal in this paper is to establish inequalities for the moments of new better than used in the moment generating function class ($NBU_{mgf}$). Using these inequalities we propose a new test for exponentiality versus $NBU_{mgf}$ class. Pitman's asymptotic relative efficiency, power and critical values of this test are calculated to assess the performance of the test. We proposed also a new test for exponentiality versus $NBU_{mgf}$ in the right censored data. Sets of real data are used as an example to elucidate the use of the proposed test for practical problems.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.277-284
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• 2000

The transformed sample Lorenz curve provides a powerful and easily computed goodness-of-fit test for exponentiality which does not depend on the unknown scale parameter. We compare the power of the transformed sample Lorenz curve statistic with the other goodness-of-fit tests for exponentiality against various alternatives through Monte Carlo methods and discuss the results.

• International Journal of Reliability and Applications
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• 제9권1호
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• pp.71-78
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• 2008

Based on the goodness of fit approach, a new test is presented for testing exponentiality versus exponential better (worse) than used (EBU (EWU)) class of life distributions. The new test is much simpler to compute, asymptotically normal, enjoys good power and performs better than previous tests in terms of power and Pitman asymptotic efficiencies for several alternatives.

• International Journal of Reliability and Applications
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• 제8권2호
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• pp.125-135
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• 2007

In this paper, testing exponentiality against new better than used in convex average and denote by (NBUCA), or its dual (NWUCA) is investigated through the U-test. The percentiles of these tests are tabulated for samples sizes n = 5(1)40. The power estimates of the test are simulated for some commonly used distributions in reliability. Pitman's asymptotic efficiency of the test is calculated and compared. Data of 40 patients suffering from blood cancer disease (Leukemia) is considered as a practical application of the proposed test in the medical sciences.

• International Journal of Reliability and Applications
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• 제14권1호
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• pp.1-9
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• 2013

A nonparametric procedure for testing exponentially against used better than aged in expectation (UBAE) class of life distributions is presented. We construct a test statistics based on scaled total time on test (TTT)-transformation, to test exponentiality against UBAE class of life distributions. The distribution of the statistic is investigated via simulation. Practical applications of the proposed test are presented.

• 응용통계연구
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• 제21권2호
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• pp.265-273
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• 2008

본 논문에서는 Kim (2001a)에서 제안한 지수분포에서의 수정된 Shapiro와 Wilk (1972) $W_E$-통계량을 중도절단자료에 적용하였다. 검정통계량은 Samanta와 Schwarz (1988)에서 $W_E$-통계량을 중도절단자료에 대해 수정한 것과 같은 방법으로 정규화 등간격(normalized spacings)을 이용하여 수정하였다. 그 결과 제안된 통계량은 귀무가설에서 중도절단이 없는 경 우와 같은 분포를 갖고 표본크기만 변하게 된다. 제안된 통계량의 검정력을 Samanta와 Schwarz (1988)의 통계량과 비교한 결과, 중도절단이 없는 경우와 마찬가지로 중도절단이 있는 경우에도 변동계수가 1보다 크거나 같은 대립가설에서 제안된 통계량은 더 좋은 검정력을 나타내었다.