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.
Similar content being viewed by others
References
Balasooriya U, Gadag V (1994) Tests for upper outliers in the two-parameter exponential distribution. J Stat Comput Simul 50: 249–259
Barnett V (1978) The study of outliers: purpose and model. Appl Stat 27: 242–250
Barnett VA, Lewis T (1994) Outliers in statistical data. Wiley, Chichester
Chikkagoudar MS, Kunchur SM (1983) Distributions of test statistics for multiple outliers in exponential samples. Commun Stat Theory Methods 12: 2127–2142
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
Dixon WJ (1950) Analysis of extreme values. Ann Math Stat 21: 488–506
Grubbs FE (1950) Sample criteria for testing outlying observations. Ann Math Stat 21: 27–58
Gupta SS (1960) Order statistics from the gamma distribution. Technometrics 2: 243–262
Harter HL (1961) Expected values of normal order statistics. Biometrika 48: 151–165
Jabbari Nooghabi M, Jabbari Nooghabi H, Nasiri P (2010) Detecting outliers in gamma distribution. Commun Stat Theory Methods 39: 698–706
Jeevanand ES, Nair NU (1998) On determining the number of outliers in exponential and pareto samples. Stat Pap 39: 277–290
Kale BK (1976) Detection of outliers. Sankhya B 38: 356–363
Kimber AC (1979) Tests for a single outlier in a gamma sample with unknown shape and scale parameters. Appl Stat 28: 243–250
Kimber AC (1982) Tests for many outliers in an exponential sample. Appl Stat 31: 263–271
Kimber AC (1988) Testing upper and lower outlier pairs in gamma samples. Commun Stat Simul 17: 1055–1072
Kimber AC, Stevens HJ (1981) The null distribution of a test for two upper outliers in an exponential samples. Appl Stat 30: 153–157
Lewis T, Fieller NRJ (1979) A recursive algorithm for null distribution for outliers: I. Gamma samples. Technometrics 21: 371–376
Likes J (1966) Distribution of Dixon’s statistics in the case of an exponential population. Metrika 11: 46–54
Likes J (1987) Some tests for k ≥ 2 upper outliers in an exponential sample. Biometr J 29: 313–324
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
McLachlan G, Krishnan T (1996) The EM algorithm and extensions. Wiley, New York
Tietjen GL, Moore RH (1972) Some Grubbs-type statistics for the detection of several outliers. Technometrics 14: 583–597
Tiku ML (1975) A new statistic for testing suspected outliers. Commun Stat 4: 737–752
Wu JW (2001) A note on determining the number of outliers in an exponential sample by least squares procedure. Stat Pap 42: 489–530
Zerbet A, Nikulin M (2003) A new statistic for detecting outliers in exponential case. J Stat Comput Simul 32: 573–583
Zhang J (1998) Tests for multiple upper or lower outliers in an exponential sample. J Appl Stat 25: 245–255
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kumar, N. A procedure for testing suspected observations. Stat Papers 54, 471–478 (2013). https://doi.org/10.1007/s00362-012-0444-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-012-0444-3