• Title, Summary, Keyword: Anderson-Darling test

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A Study on Empirical Distribution Function with Unknown Shape Parameter and Extreme Value Weight for Three Parameter Weibull Distribution (3변수 Weibull 분포형의 형상매개변수 및 극치값 가중치를 고려한 EDF 검정에 대한 연구)

  • Kim, Taereem;Shin, Hongjoon;Heo, Jun-Haeng
    • Journal of Korea Water Resources Association
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    • v.46 no.6
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    • pp.643-653
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    • 2013
  • The most important procedure in frequency analysis is to determine the appropriate probability distribution and to estimate quantiles for a given return period. To perform the frequency analysis, the goodness-of-fit tests should be carried out for judging fitness between obtained data from empirical probability distribution and assumed probability distribution. The previous goodness-of-fit could not consider enough extreme events from the recent climate change. In this study, the critical values of the modified Anderson-Darling test statistics were derived for 3-parameter Weibull distribution and power test was performed to evaluate the performance of the suggested test. Finally, this method was applied to 50 sites in South Korea. The result shows that the power of modified Anderson-Darling test has better than other existing goodness-of-fit tests. Thus, modified Anderson-Darling test will be able to act as a reference of goodness-of-fit test for 3-parameter Weibull model.

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.

An Analysis on Noise Reduction Effects of Two-Layer Low Noise Pavements using Statistical Methods (통계적 방법을 이용한 복층 저소음포장의 소음저감효과 분석)

  • Lee, Sang Hyuk;Han, Dae Seok;Yoo, In Kyoon;Lee, Soo Hyung
    • International Journal of Highway Engineering
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    • v.19 no.6
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    • pp.1-11
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    • 2017
  • PURPOSES : The purpose of this study is to compare noise reduction quantities between before/after two-layer low noise pavement implementation using equivalent noise level analysis and to analyze the noise reduction effects of the two layer low noise pavement with a statistical method such as the Anderson-Darling Test. METHODS : In order to compare and to analyze noise reduction effects between before/after two-layer low noise pavement implementation, data acquisition as noise levels on a roadside and an apartment rooftop was conducted in the study area. The equivalent noise level was estimated in order to compare noise reduction quantities and the Anderson-Darling Test was carried out for estimating noise reduction effects of the two-layer low noise pavement. RESULTS : The equivalent noise levels of before/after two-layer low noise pavement implementation for the roadside during the daytime are 65.355 dB and 63.520 dB and during the nighttime are 62.463 dB and 59.088 dB. The equivalent noise levels for the apartment rooftop during daytime are 57.301 dB and 59.088 dB and during the nighttime are 54.616 dB and 52.464 dB. Also two-layer low noise pavement decreased the noise reduction effects estimated with the statistical method as the Anderson-Darling test for the roadside during the daytime by around 66.68% and decreased noise reduction effects on the roadside during the nighttime by 0.70%. Moreover it reduced noise reduction effects in the apartment rooftop during the daytime and nighttime by 0% and 96.32%, respectively. CONCLUSIONS : Based on the result of this study, two-layer low noise pavement can positively affect noise reduction during both the daytime and nighttime according to the results of estimating the equivalent noise levels and the Anderson-Darling test.

Tests based on EDF statistics for randomly censored normal distributions when parameters are unknown

  • Kim, Namhyun
    • Communications for Statistical Applications and Methods
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    • v.26 no.5
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    • pp.431-443
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    • 2019
  • Goodness-of-fit techniques are an important topic in statistical analysis. Censored data occur frequently in survival experiments; therefore, many studies are conducted when data are censored. In this paper we mainly consider test statistics based on the empirical distribution function (EDF) to test normal distributions with unknown location and scale parameters when data are randomly censored. The most famous EDF test statistic is the Kolmogorov-Smirnov; in addition, the quadratic statistics such as the $Cram{\acute{e}}r-von$ Mises and the Anderson-Darling statistic are well known. The $Cram{\acute{e}}r-von$ Mises statistic is generalized to randomly censored cases by Koziol and Green (Biometrika, 63, 465-474, 1976). In this paper, we generalize the Anderson-Darling statistic to randomly censored data using the Kaplan-Meier estimator as it was done by Koziol and Green. A simulation study is conducted under a particular censorship model proposed by Koziol and Green. Through a simulation study, the generalized Anderson-Darling statistic shows the best power against almost all alternatives considered among the three EDF statistics we take into account.

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.

Derivation of Modified Anderson-Darling Test Statistics and Power Test for the Gumbel Distribution (Gumbel 분포형의 수정 Anderson-Darling 검정통계량 유도 및 기각력 검토)

  • Shin, Hong-Joon;Sung, Kyung-Min;Heo, Jun-Haeng
    • Journal of Korea Water Resources Association
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    • v.43 no.9
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    • pp.813-822
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    • 2010
  • An important problem in frequency analysis is the estimation of the quantile for a certain return period. In frequency analysis an assumed probability distribution is fitted to the observed sample data to estimate the quantile at the upper tail corresponding to return periods which are usually much larger than the record length. In most cases, the selection of an appropriate probability distribution is based on goodness of fit tests. The goodness of fit test method can be described as a method for examining how well sample data agrees with an assumed probability distribution as its population. However it gives generally equal weight to differences between empirical and theoretical distribution functions corresponding to all the observations. In this study, the modified Anderson-Darling (AD) test statistics are provided using simulation and the power study are performed to compare the efficiency of other goodness of fit tests. The power test results indicate that the modified AD test has better rejection performances than the traditional tests. In addition, the applications to real world data are discussed and shows that the modified AD test may be a powerful test for selecting an appropriate distribution for frequency analysis when extreme cases are considered.

Goodness-of-fit test for the gumbel distribution based on the generalized Lorenz curve (일반화된 로렌츠 곡선을 기반으로 한 Gumbel 분포의 적합도 검정)

  • Lee, Kyeongjun
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.4
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    • pp.733-742
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    • 2017
  • There are many areas of applications where Gumbel distribution are employed such as environmental sciences, system reliability and hydrology. The goodness-of-fit test for Gumbel distribution is very important in environmental sciences, system reliability and hydrology data analysis. Therefore, we propose the two test statistics to test goodness-of-fit for the Gumbel distribution based on the generalized Lorenz curve. We compare the new test statistic with the Anderson - Darling test, Cramer - vonMises test, and modified Anderson - Darling test in terms of the power of the test through by Monte Carlo method. As a result, the new test statistics are more powerful than the other test statistics. Also, we propose new graphic method to goodness-of-fit test for the Gumbel distribution based on the generalized Lorenz curve.

An Anderson-Darling Goodness-of-Fit Test for the Gamma Distribution

  • Won, Hyung-Gyoo
    • Journal of the Korean Society for Quality Management
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    • v.24 no.4
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    • pp.103-111
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    • 1996
  • This paper provides a test of the composite hypothesis that a random sample is (two parameter) gamma distributed when both the scale and shape parameters are estimated from the data. The test statistic is a variant of the usual Anderson-Darling statistic, the primary difference being that the statistic is based on the maximum likelihood estimator of the shape parameter of the assumed gamma distribution. The percentage points are developed via simulation and are presented graphically. Examples are provided.

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A Study on Selection of Distribution Function for Reliability Prediction Using Accelerated Life Test Data (가속 수명시험 데이터를 기반으로 하는 신뢰성 예측에 적합한 분포 함수 선택에 관한 연구)

  • Kim Ji-Hun;Park Dong-Gue;Han Hyun-Kak
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.7 no.3
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    • pp.393-397
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    • 2006
  • The study about Accelerated Life Test and analysis of failed data is increased in order to predict and evaluate reliability of products, according as the development cycle of products is reduced. Therefore, the decision of optimal distribution function about failed data for accurate analysis of failed data and test condition for Accelerated Life Test is very important. This paper compares Anderson-Darling method with Likelihood Function method for the decision of optimal distribution function about failed data. Anderson-Darling considers only failed data and Likelihood Function considers both failed data and life-stress relationship in decision of distribution function. In the results of comparison about two methods, we found that the distribution function chosen by each method is different and the life time predicted by each decided distribution function is different.

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A View on the Validity of Central Limit Theorem: An Empirical Study Using Random Samples from Uniform Distribution

  • Lee, Chanmi;Kim, Seungah;Jeong, Jaesik
    • Communications for Statistical Applications and Methods
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    • v.21 no.6
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    • pp.539-559
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    • 2014
  • We derive the exact distribution of summation for random samples from uniform distribution and then compare the exact distribution with the approximated normal distribution obtained by the central limit theorem. To check the similarity between two distributions, we consider five existing normality tests based on the difference between the target normal distribution and empirical distribution: Anderson-Darling test, Kolmogorov-Smirnov test, Cramer-von Mises test, Shapiro-Wilk test and Shaprio-Francia test. For the purpose of comparison, those normality tests are applied to the simulated data. It can sometimes be difficult to derive an exact distribution. Thus, we try two different transformations to find out which transform is easier to get the exact distribution in terms of calculation complexity. We compare two transformations and comment on the advantages and disadvantages for each transformation.