Exact tests for outliers in Laplace samples

References

• Andrews, D. F., P. J. Bickel, F. R. Hampel, P. J. Huber, W. H. Rogers, and J. W. Tukey. 1972. Robust estimates of location. Princeton, NJ: Princeton University Press.
   Google Scholar
• Anscombe, F. J. 1960. Rejection of outliers. Technometrics 2 (2):123–46. doi:10.1080/00401706.1960.10489888.
   Google Scholar
• Arnold, B. C., N. Balakrishnan, and H. N. Nagaraja. 1992. A first course in order statistics. New York: Wiley.
   Google Scholar
• Bain, L. J., and M. Engelhardt. 1973. Interval estimation for the two-parameter double exponential distribution. Technometrics 15 (4):875–87. doi:10.1080/00401706.1973.10489120.
   Web of Science ®Google Scholar
• Balakrishnan, N., and C. D. Cutler. 1995. Maximum likelihood estimation of the Laplace parameters based on Type-II censored samples. In Statistical theory and applications: Papers in honor of Herbert A. David, ed. H. N. Nagaraja, P. K. Sen, and D. F. Morrison, 145–51. New York: Springer.
   Google Scholar
• Balakrishnan, N., and X. Zhu. 2016. Exact likelihood-based point and interval estimation for Laplace distribution based on Type-II right censored samples. Journal of Statistical Computation and Simulation 86 (1):29–54. doi:10.1080/00949655.2014.993637.
   Web of Science ®Google Scholar
• Barnett, V. A., and T. Lewis. 1994. Outliers in statistical data, 2nd ed. Chichester: Wiley.
   Google Scholar
• Childs, A. 1996. Advances in statistical inference and outliers related issues. Ph.D. diss., McMaster University, Hamilton, Canada.
   Google Scholar
• Childs, A., and N. Balakrishnan. 1996. Conditional inference procedures for the Laplace distribution based on Type-II right censored samples. Statistics & Probability Letters 31 (1):31–9. doi:10.1016/S0167-7152(96)00010-7.
   Web of Science ®Google Scholar
• Childs, A., and N. Balakrishnan. 1997a. Some extensions in the robust estimation of parameters of exponential and double exponential distributions in the presence of multiple outliers. In Handbook of statistics – robust inference, vol. 15, eds. C. R. Rao and G. S. Maddala, 201–35. Amsterdam: North-Holland.
   Google Scholar
• Childs, A., and N. Balakrishnan. 1997b. Maximum likelihood estimation of Laplace parameters based on general Type-II censored examples. Statistical Papers 38 (3):343–9. doi:10.1007/BF02925273.
   Web of Science ®Google Scholar
• David, H. A., H. O. Hartley, and E. S. Pearson. 1954. The distribution of the ratio, in a single normal sample, of range to standard deviation. Biometrika 41 (3–4):482–93. doi:10.1093/biomet/41.3-4.482.
   Web of Science ®Google Scholar
• Dixon, W. J. 1950. Analysis of extreme values. The Annals of Mathematical Statistics 21 (4):488–506. doi:10.1214/aoms/1177729747.
   Google Scholar
• Dixon, W. J. 1951. Ratios involving extreme values. The Annals of Mathematical Statistics 22 (1):68–78. doi:10.1214/aoms/1177729693.
   Google Scholar
• Dixon, W. J. 1953. Processing data for outliers. Biometrics 9 (1):74–89. doi:10.2307/3001634.
   Web of Science ®Google Scholar
• Grubbs, F. E. 1950. Sample criteria for testing outlying observations. The Annals of Mathematical Statistics 21 (1):27–58. doi:10.1214/aoms/1177729885.
   Google Scholar
• Grubbs, F. E. 1969. Procedures for detecting outlying observations in samples. Technometrics 11 (1):1–21. doi:10.1080/00401706.1969.10490657.
   Web of Science ®Google Scholar
• Grubbs, F. E., and G. Beck. 1972. Extension of sample sizes and percentage points for significance tests of outlying observations. Technometrics 14 (4):847–54. doi:10.1080/00401706.1972.10488981.
   Web of Science ®Google Scholar
• Hoaglin, D. C., F. Mosteller, and J. W. Tukey, eds. 1983. Understanding robust and exploratory data analysis. New York: Wiley.
   Google Scholar
• Huffer, F. 1988. Divided differences and the joint distribution of linear combinations of spacings. Journal of Applied Probability 25 (2):346–54. doi:10.1017/S0021900200040985.
   Web of Science ®Google Scholar
• Huffer, F. W., and C. T. Lin. 2001. Computing the joint distribution of general linear combinations of spacings or exponential variates. Statistica Sinica 11 (4):1141–57.
   Web of Science ®Google Scholar
• Huffer, F. W., and C. T. Lin. 2006. Linear combinations of spacings. In Encyclopedia of Statistical Sciences, ed. by S. Kotz, N. Balakrishnan, C. B. Read, and B. Vidakovic, vol. 12, 2nd ed., 7866–75. Hoboken, New Jersey: Wiley.
   Google Scholar
• Iliopoulos, G., and N. Balakrishnan. 2009. Conditional independence of blocked ordered data. Statistics & Probability Letters 79 (8):1008–15. doi:10.1016/j.spl.2008.12.005.
   Web of Science ®Google Scholar
• Iliopoulos, G., and S. M. T. K. MirMostafaee. 2014. Exact prediction intervals for order statistics from the Laplace distribution based on the maximum likelihood estimators. Statistics 48 (3):575–92. doi:10.1080/02331888.2013.766795.
   Web of Science ®Google Scholar
• Johnson, N. L., S. Kotz, and N. Balakrishnan. 1995. Continuous univariate distributions, vol. 2, 2nd ed. New York: Wiley.
   Google Scholar
• Kotz, S., T. Kozubowski, and K. Podgorski. 2001. The Laplace distribution and generalizations: A revisit with applications to communications, economics, engineering, and finance. Boston: Birkhauser.
   Google Scholar
• Kumar, N. 2019. Exact distributions of tests of outliers for exponential samples. Statistical Papers 60 (6):2031–61. doi:10.1007/s00362-017-0908-6.
   Web of Science ®Google Scholar
• Kumar, N., and C. T. Lin. 2017. Testing for multiple upper and lower outliers in an exponential sample. Journal of Statistical Computation and Simulation 87 (5):870–81. doi:10.1080/00949655.2016.1232723.
   Web of Science ®Google Scholar
• Lin, C. T., and N. Balakrishnan. 2009. Exact computation of the null distribution of a test for multiple outliers in an exponential sample. Computational Statistics & Data Analysis 53 (9):3281–90.
   Web of Science ®Google Scholar
• Lin, C. T., and N. Balakrishnan. 2014. Tests for multiple outliers from an exponential population. Communications in Statistics – Simulation and Computation 43 (4):706–22. doi:10.1080/03610918.2012.714030.
   Web of Science ®Google Scholar
• Lin, C. T., B. Y. Lee, and N. Balakrishnan. 2019a. On the computation of distributions of linear combinations of Laplace order statistics and their applications. Communications in Statistics – Simulation and Computation 48 (10):3031–55. doi:10.1080/03610918.2018.1473590.
   Web of Science ®Google Scholar
• Lin, C. T., Y. C. Lee, and N. Balakrishnan. 2019b. Package mTEXO for testing the presence of outliers in exponential samples. Computational Statistics 34 (2):803–18. doi:10.1007/s00180-018-0843-6.
   Web of Science ®Google Scholar
• Lin, C. T., and S. C. Wang. 2015. Discordancy tests for two-parameter exponential samples. Statistical Papers 56 (2):569–82. doi:10.1007/s00362-014-0597-3.
   Web of Science ®Google Scholar
• Murphy, R. B. 1951. On tests for outlying observations. Ph.D. diss., Department of Mathematics, Princeton University, Princeton, New Jersey.
   Google Scholar
• Tiku, M. L., W. Y. Tan, and N. Balakrishnan. 1986. Robust inference. New York: Marcel Dekker.
   Google Scholar
• Verma, S. P., and A. Quiroz-Ruiz. 2006a. Critical values for six Dixon tests for outliers in normal samples up to sizes 100, and applications in science and engineering. Revista Mexicana de Ciencias Geologicas 23 (2):133–61.
   Web of Science ®Google Scholar
• Verma, S. P., and A. Quiroz-Ruiz. 2006b. Critical values for 22 discordancy test variants for outliers in normal samples up to sizes 100, and applications in science and engineering. Revista Mexicana de Ciencias Geologicas 23 (3):302–19.
   Web of Science ®Google Scholar
• Zhu, X., and N. Balakrishnan. 2016. Exact inference for Laplace quantile, reliability, and cumulative hazard functions based on Type-II censored data. IEEE Transactions on Reliability 65 (1):164–78. doi:10.1109/TR.2015.2451617.
   Web of Science ®Google Scholar