• Title, Summary, Keyword: Cramer von-Mises

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EDF 통계량을 이용한 다변량 정규성 검정

  • Kim, Nam-Hyeon
    • Proceedings of the Korean Statistical Society Conference
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    • pp.31-36
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    • 2005
  • EDF에 근거한 Cramer-von Mises 형태의 통계량을 합교원리를 이용하여 다변량으로 일반화한다. 그리고 제안된 통계량의 귀무가설에서의 극한분포를 적절한 공분산함수를 가진 가우스 과정의 적분의 형태로 표현하고 통계량의 근사적인 계산방법을 고려한다.

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Goodness-of-fit Tests for the Weibull Distribution Based on the Sample Entropy

  • Kang, Suk-Bok;Lee, Hwa-Jung
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.1
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    • pp.259-268
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    • 2006
  • For Type-II censored sample, we propose three modified entropy estimators based on the Vasieck's estimator, van Es' estimator, and Correa's estimator. We also propose the goodness-of-fit tests of the Weibull distribution based on the modified entropy estimators. We simulate the mean squared errors (MSE) of the proposed entropy estimators and the powers of the proposed tests. We also compare the proposed tests with the modified Kolmogorov-Smirnov and Cramer-von-Mises tests which were proposed by Kang et al. (2003).

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Tests for the exponential distribution based on Type-II censored samples

  • Kang, Suk-Bok;Cho, Young-Suk;Choi, Sei-Yeon
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.2
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    • pp.367-376
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    • 2003
  • Two explicit estimators of the scale parameter in an exponential distribution based on Type-II censored samples are proposed by appropriately approximating the likelihood function. Then two type tests, including the modified Cramer-von Mises test and Kolmogorov-Smirnov test are developed for the exponential distribution based on Type-II censored samples by using the proposed estimators. For each test, Monte Carlo techniques are used to generate critical values. The powers of these tests are investigated under several alternative distributions.

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Testing Goodness of Fit in Nonparametric Function Estimation Techniques for Proportional Hazards Model

  • Kim, Jong-Tae
    • Communications for Statistical Applications and Methods
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    • v.4 no.2
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    • pp.435-444
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    • 1997
  • The objective of this study is to investigate the problem of goodness of fit testing based on nonparametric function estimation techniques for the random censorship model. The small and large sample properties of the proposed test, $E_{mn}$, were investigated and it is shown that under the proportional hazard model $E_{mn}$ has higher power compared to the powers of the Kolmogorov -Smirnov, Kuiper, Cramer-von Mises, and analogue of the Cramer-von Mises type test statistic.

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Modified Test Statistic for Identity of Two Distribution on Credit Evaluation (신용평가에서 두 분포의 동일성 검정에 대한 수정통계량)

  • Hong, C.S.;Park, H.S.
    • The Korean Journal of Applied Statistics
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    • v.22 no.2
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    • pp.237-248
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    • 2009
  • The probability of default on the credit evaluation study is represented as a linear combination of two distributions of default and non-default, and the distribution of the probability of default are generally known in most cases. Except the well-known Kolmogorov-Smirnov statistic for testing the identity of two distribution, Kuiper, Cramer-Von Mises, Anderson-Darling, and Watson test statistics are introduced in this work. Under the assumption that the population distribution is known, modified Cramer-Von Mises, Anderson-Darling, and Watson statistics are proposed. Based on score data generated from various probability density functions of the probability of default, the modified test statistics are discussed and compared.

Test for the Exponential Distribution Based on Multiply Type-II Censored Samples

  • Kang, Suk-Bok;Lee, Sang-Ki
    • Communications for Statistical Applications and Methods
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    • v.13 no.3
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    • pp.537-550
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    • 2006
  • In this paper, we develope three modified empirical distribution function type tests, the modified Cramer-von Mises test, the modified Anderson-Darling test, and the modified Kolmogorov-Smirnov test for the two-parameter exponential distribution with unknown parameters based on multiply Type-II censored samples. For each test, Monte Carlo techniques are used to generate the critical values. The powers of these tests are also investigated under several alternative distributions.

Goodness of Fit Testing for Exponential Distribution in Step-Stress Accelerated Life Testing (계단충격가속수명시험에서의 지수분포에 대한 적합도검정)

  • Jo, Geon-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.5 no.2
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    • pp.75-85
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    • 1994
  • In this paper, I introduce the goodness-of-fit test statistics for exponential distribution using accelerated life test data. The ALT lifetime data were obtained by assuming step-stress ALT model, specially TRV model introduced by DeGroot and Goel(1979). The critical values are obtained for proposed test statistics, Kolmogorov-Smirnov, Kuiper, Watson, Cramer-von Mises, Anderson-Darling type, under various sample sizes and significance levels. The powers of the five test statistic are compared through Monte-Cairo simulation technique.

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A Study on Goodness of Fit Test in Accelerated Life Tests (가속수명시험에 대한 적합도 검정에 관한 연구)

  • Lee, Woo-Dong;Cho, Geon-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.7 no.1
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    • pp.37-46
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    • 1996
  • In this paper, we introduce the goodness of fit test procedure for lifetime distribution using step stress accelerated lifetime data. Using the nonpapametric estimate of acceleration factor, we prove the strong consistence of empirical distribution function under null hypothesis. The critical vailues of Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises statistics are computed when the lifetime distibution is assumed to be exponential and Weibull. The power of test statistics are compared through Monte-Cairo simulation study.

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INDEPENDENCE TEST FOR BIVARIATE CENSORED DATA UNDER UNIVARIATE CENSORSHIP

  • Kim, Jin-Heum;Cai, Jian-Wen
    • Journal of the Korean Statistical Society
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    • v.32 no.2
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    • pp.163-174
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    • 2003
  • We propose a test for independence of bivariate censored data under univariate censorship. To do this, we first introduce a process defined by the difference between bivariate survival function estimator proposed by Lin and Ying (1993) and the product of the product-limit estimators (Kaplan and Meier, 1958) for the marginal survival functions, and derive its asymptotic properties under the null hypothesis of independence. We propose a Cramer-von Mises-type test procedure based on the process . We conduct simulation studies to investigate the finite-sample performance of the proposed test and illustrate the proposed test with a real example.