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Exact computation of the null distribution of a test for multiple outliers in an exponential sample

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  • Lin, Chien-Tai
  • Balakrishnan, N.

Abstract

Through a systematic application of the recursion of Huffer [Huffer, F., 1988. Divided differences and the joint distribution of linear combinations of spacings. Journal of Applied Probability 25, 346-354], we present an algorithm for evaluating the exact null distribution of the test statistic proposed by Kimber [Kimber, A.C., 1982. Tests for many outliers in an exponential sample. Applied Statistics 31, 263-271] for the testing of up to k upper outliers for discordancy in exponential samples. This method presents another way of obtaining the exact null distribution of the test statistic without first obtaining their joint density. The advantage of this approach is in its generality and also in its ease of use. In addition, it can provide critical values for the test statistic that are accurate to any required degree of precision. Similar results for the sequential testing of up to k lower outliers for discordancy are also presented.

Suggested Citation

  • Lin, Chien-Tai & Balakrishnan, N., 2009. "Exact computation of the null distribution of a test for multiple outliers in an exponential sample," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3281-3290, July.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3281-3290
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    References listed on IDEAS

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    1. A. C. Kimber & H. J. Stevens, 1981. "The Null Distribution of a Test for Two Upper Outliers in an Exponential Sample," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(2), pages 153-157, June.
    2. A. C. Kimber, 1982. "Tests for Many Outliers in an Exponential Sample," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 263-271, November.
    3. D. Kabe, 1970. "Testing outliers from an exponential population," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 15(1), pages 15-18, December.
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    Cited by:

    1. Nirpeksh Kumar, 2013. "A procedure for testing suspected observations," Statistical Papers, Springer, vol. 54(2), pages 471-478, May.
    2. Vilijandas Bagdonavičius & Linas Petkevičius, 2020. "Multiple Outlier Detection Tests for Parametric Models," Mathematics, MDPI, vol. 8(12), pages 1-23, December.
    3. Chien-Tai Lin & Ying-Chen Lee & Narayanaswamy Balakrishnan, 2019. "Package mTEXO for testing the presence of outliers in exponential samples," Computational Statistics, Springer, vol. 34(2), pages 803-818, June.
    4. Chien-Tai Lin & Shih-Chun Wang, 2015. "Discordancy tests for two-parameter exponential samples," Statistical Papers, Springer, vol. 56(2), pages 569-582, May.
    5. Nirpeksh Kumar, 2019. "Exact distributions of tests of outliers for exponential samples," Statistical Papers, Springer, vol. 60(6), pages 2031-2061, December.

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