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A procedure for testing suspected observations

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Abstract

The problem of multiple outliers detection in one-parameter exponential family is considered. The outlier detection procedure involves two estimates of scale parameter which are obtained by maximizing two log-likelihoods; the complete data log-likelihood and its conditional expectation given suspected observations. The procedure is also applied to the exponential and normal samples.

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References

  • Balasooriya U, Gadag V (1994) Tests for upper outliers in the two-parameter exponential distribution. J Stat Comput Simul 50: 249–259

    Article  MATH  Google Scholar 

  • Barnett V (1978) The study of outliers: purpose and model. Appl Stat 27: 242–250

    Article  Google Scholar 

  • Barnett VA, Lewis T (1994) Outliers in statistical data. Wiley, Chichester

    MATH  Google Scholar 

  • Chikkagoudar MS, Kunchur SM (1983) Distributions of test statistics for multiple outliers in exponential samples. Commun Stat Theory Methods 12: 2127–2142

    Article  MathSciNet  MATH  Google Scholar 

  • David HA, Hartley HO, Pearson ES (1954) The distribution of the ratio, in a single normal sample, of range to standard deviation. Biometrika 41: 482–483

    MathSciNet  MATH  Google Scholar 

  • Dixon WJ (1950) Analysis of extreme values. Ann Math Stat 21: 488–506

    Article  Google Scholar 

  • Grubbs FE (1950) Sample criteria for testing outlying observations. Ann Math Stat 21: 27–58

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta SS (1960) Order statistics from the gamma distribution. Technometrics 2: 243–262

    Article  MathSciNet  MATH  Google Scholar 

  • Harter HL (1961) Expected values of normal order statistics. Biometrika 48: 151–165

    MathSciNet  Google Scholar 

  • Jabbari Nooghabi M, Jabbari Nooghabi H, Nasiri P (2010) Detecting outliers in gamma distribution. Commun Stat Theory Methods 39: 698–706

    Article  MathSciNet  MATH  Google Scholar 

  • Jeevanand ES, Nair NU (1998) On determining the number of outliers in exponential and pareto samples. Stat Pap 39: 277–290

    Article  MATH  Google Scholar 

  • Kale BK (1976) Detection of outliers. Sankhya B 38: 356–363

    MATH  Google Scholar 

  • Kimber AC (1979) Tests for a single outlier in a gamma sample with unknown shape and scale parameters. Appl Stat 28: 243–250

    Article  MATH  Google Scholar 

  • Kimber AC (1982) Tests for many outliers in an exponential sample. Appl Stat 31: 263–271

    Article  MathSciNet  MATH  Google Scholar 

  • Kimber AC (1988) Testing upper and lower outlier pairs in gamma samples. Commun Stat Simul 17: 1055–1072

    Article  MATH  Google Scholar 

  • Kimber AC, Stevens HJ (1981) The null distribution of a test for two upper outliers in an exponential samples. Appl Stat 30: 153–157

    Article  MathSciNet  MATH  Google Scholar 

  • Lewis T, Fieller NRJ (1979) A recursive algorithm for null distribution for outliers: I. Gamma samples. Technometrics 21: 371–376

    Article  MathSciNet  MATH  Google Scholar 

  • Likes J (1966) Distribution of Dixon’s statistics in the case of an exponential population. Metrika 11: 46–54

    Article  MathSciNet  MATH  Google Scholar 

  • Likes J (1987) Some tests for k ≥ 2 upper outliers in an exponential sample. Biometr J 29: 313–324

    Article  MathSciNet  MATH  Google Scholar 

  • Lin CT, Balakrishnan N (2009) Exact computation of the null distribution of a test for multiple outliers in an exponential sample. Comput Stat Data Anal 53: 3281–3290

    Article  MathSciNet  MATH  Google Scholar 

  • McLachlan G, Krishnan T (1996) The EM algorithm and extensions. Wiley, New York

    Google Scholar 

  • Tietjen GL, Moore RH (1972) Some Grubbs-type statistics for the detection of several outliers. Technometrics 14: 583–597

    Article  Google Scholar 

  • Tiku ML (1975) A new statistic for testing suspected outliers. Commun Stat 4: 737–752

    MathSciNet  MATH  Google Scholar 

  • Wu JW (2001) A note on determining the number of outliers in an exponential sample by least squares procedure. Stat Pap 42: 489–530

    Article  MATH  Google Scholar 

  • Zerbet A, Nikulin M (2003) A new statistic for detecting outliers in exponential case. J Stat Comput Simul 32: 573–583

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang J (1998) Tests for multiple upper or lower outliers in an exponential sample. J Appl Stat 25: 245–255

    Article  MATH  Google Scholar 

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Correspondence to Nirpeksh Kumar.

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Kumar, N. A procedure for testing suspected observations. Stat Papers 54, 471–478 (2013). https://doi.org/10.1007/s00362-012-0444-3

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  • DOI: https://doi.org/10.1007/s00362-012-0444-3

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