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Exact distributions of tests of outliers for exponential samples

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  • Nirpeksh Kumar

    (Banaras Hindu University)

Abstract

In this paper, we propose an algorithm to derive the exact distributions of discordancy tests for exponential samples under the slippage alternative providing that their survival functions involve the linear combinations of independent and identically distributed exponential random variables with arbitrary real coefficients. In addition, we define the various performance measures in terms of conditional probabilities that the observed value of the test statistic exceeds the critical value given that the contaminants have the specific position numbers in the ordered sample. These make possible to calculate various performance measures of discordancy tests for the exponential samples to any desired degree of accuracy. For the purpose of illustration, we derive the distributions of the maximum likelihood ratio tests for testing single and multiple outliers in the exponential samples and then we calculate their performance measures accurately to six decimal places. Moreover, the definitions of the performance criteria are not restricted to the discordancy tests for exponential samples only, they are also equally applicable to the discordancy tests for samples from other distributions.

Suggested Citation

  • Nirpeksh Kumar, 2019. "Exact distributions of tests of outliers for exponential samples," Statistical Papers, Springer, vol. 60(6), pages 2031-2061, December.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:6:d:10.1007_s00362-017-0908-6
    DOI: 10.1007/s00362-017-0908-6
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    References listed on IDEAS

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    1. Nirpeksh Kumar, 2013. "A procedure for testing suspected observations," Statistical Papers, Springer, vol. 54(2), pages 471-478, May.
    2. P. Prescott, 1979. "Critical Values for a Sequential Test for Many Outliers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(1), pages 36-39, March.
    3. Douglas M. Hawkins, 1980. "Critical Values for Identifying Outliers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 95-96, March.
    4. 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.
    5. Nirpeksh Kumar, 2015. "Testing of Suspected Observations in an Exponential Sample With Unknown Origin," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(17), pages 3668-3679, September.
    6. 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.
    7. Jin Zhang, 1998. "Tests for multiple upper or lower outliers in an exponential sample," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(2), pages 245-255.
    8. S. Lalitha & Nirpeksh Kumar, 2012. "Multiple outlier test for upper outliers in an exponential sample," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1323-1330, November.
    9. Chien-Tai Lin & Shih-Chun Wang, 2015. "Discordancy tests for two-parameter exponential samples," Statistical Papers, Springer, vol. 56(2), pages 569-582, May.
    10. 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.
    11. 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. Okhli, Kheirolah & Jabbari Nooghabi, Mehdi, 2023. "On the three-component mixture of exponential distributions: A Bayesian framework to model data with multiple lower and upper outliers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 480-500.
    2. Okhli, Kheirolah & Jabbari Nooghabi, Mehdi, 2021. "On the contaminated exponential distribution: A theoretical Bayesian approach for modeling positive-valued insurance claim data with outliers," Applied Mathematics and Computation, Elsevier, vol. 392(C).

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