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15-09-2016

Estimation of the Lomax Distribution in the Presence of Outliers

Author: Mehdi Jabbari Nooghabi

Published in: Annals of Data Science | Issue 4/2016

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Abstract

In this paper, we find the moment, maximum likelihood, least squares and weighted least squares estimators of the parameters of Lomax distribution in the presence of outliers. Also, the mixture estimator of these four methods is derived. Further, we discuss about the efficiency of the estimators. Analysis of a simulated data set and an actual example from an insurance company has been presented for illustrative purposes.

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Abramowitz M, Stegun AI (1970) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications, New York

Afify EDE (2006) Order statistics from Pareto distribution. J Appl Sci 6(10):2151–2157CrossRef

Ahmed A (1991) Characterization of beta, binomial and Poisson distributions. IEEE Trans Reliab 40:290–295CrossRef

Ahsanullah M (1991) Record values of Lomax distribution. Stat Ned 41(1):21–29CrossRef

Anscombe FJ (1960) Rejection of outliers. Technometrics 2:123–147CrossRef

Al-Zahrani B, Al-Sobhi M (2013) On parameters estimation of Lomax distribution under general progressive censoring. J Qual Reliab Eng 2013:1–7CrossRef

Arnold BC (1983) The Pareto distribution. International Cooperative Publishing House, Fairland

Arnold BC, Castillo E, Sarabia JM (1998) Bayesian analysis for classical distributions using conditionally specified priors. Sankhya B 60(2):228–245

Asrabadi BR (1990) Estimation in the Pareto distribution. Metrika 37:199–205CrossRef

10.

Balakrishnan N, Ahsanullah M (1994) Relations for single and product moments of record values from Lomax distribution. Sankhya-B 56(2):140–146

11.

Balkema A, Haan L (1974) Residual life time at great age. Ann Probab 2(5):792–804CrossRef

12.

Barnett V, Lewis T (1984) Outliers in statistical data. Wiley, New York

13.

Bryson MC (1974) Heavy-tailed distributions: properties and tests. Technometrics 16(1):61–68CrossRef

14.

Chikkagoudar MS, Kunchur SH (1980) Estimation of the mean of an exponential distribution in the presence of an outlier. Can J Stat 8:59–63CrossRef

15.

Childs A, Balakrishnan N, Moshref M (2001) Order statistics from non-identical right-truncated Lomax random variables with applications. Stat Papers 42(2):187–206CrossRef

16.

Cramer E, Schmiedt AB (2011) Progressively type-II censored competing risks data from Lomax distributions. Comput Stat Data Anal 55(3):1285–1303CrossRef

17.

Dixit UJ (1987) Characterization of the gamma distribution in the presence of \(k\) outliers. Bull. Bombay Math Colloq 4:54–59

18.

Dixit UJ (1989) Estimation of the parameters of the gamma distribution in the presence of outliers. Commun Stat Theory Methods 18(8):3071–3085CrossRef

19.

Dixit UJ, Jabbari Nooghabi M (2010) Efficient estimation in the Pareto distribution. Stat Methodol 7(6):687–691CrossRef

20.

Dixit UJ, Jabbari Nooghabi M (2011) Efficient estimation in the Pareto distribution with the presence of outliers. Stat Methodol 8(4):340–355CrossRef

21.

Dixit UJ, Jabbari Nooghabi M (2011) Efficient estimation of the parameters of the Pareto distribution in the presence of outliers. Commun Korean Stat Soc 18(6):817–835

22.

El-Din MM, Okasha HM, Al-Zahrani B (2013) Empirical bayes estimators of reliability performances using progressive type-II censoring from Lomax model. J Adv Res Appl Math 5(1):74–83CrossRef

23.

Ferguson TS (1961) On the rejection of outliers. In: Proc. 4th Berkeley symposium on mathematical statistics and probability, vol 1, pp 253–287

24.

Galambos J, Kotz S (1978) Characterization of probability distributions. In: Lecture notes in mathematics, vol 675. Springer, Berlin

25.

Ghitany ME, Al-Awadhi FA, Alkhalfan LA (2007) Marshall–Olkin extended lomax distribution and its application to censored data. Commun Stat Theory Methods 36(10):1855–1866CrossRef

26.

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

27.

Grubbs FE (1969) Procedures for detecting outlying observations in samples. Technometrics 11:1–21CrossRef

28.

Harris CM (1968) The Pareto distribution as a queue series discipline. Oper Res 16:307–313CrossRef

29.

Hawkins DM (1980) Identification of outliers. Chapman and Hall, LondonCrossRef

30.

Howlader HA, Hossain AM (2002) Bayesian survival estimation of Pareto distribution of the second kind based on failurecensored data. Comput Stat Data Anal 38(3):301–314CrossRef

31.

Jabbari Nooghabi M, Khaleghpanah Nooghabi E (2016) On entropy of a Pareto distribution in the presence of outliers. Commun Stat - Theory Methods 45(17):5234–5250

32.

Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distribution, vol 2, 2nd edn. Wiley, New York

33.

Joshi PC (1972) Efficient estimation of mean of an exponential distribution when an outlier is present. Technometrics 15:137–143CrossRef

34.

Kale BK, Sinha SK (1971) Estimation of expected life in the presence of an outlier observation. Technometrics 13:755–759CrossRef

35.

Kendall MG, Buckland WR (1957) A dictionary of statistical terms. Longman, London

36.

Kern MD (1983) Minimum varince unbaised estimation in the Pareto distribution. Metrika 30:15–19CrossRef

37.

Khan AH, Abuammoh AM (1999) Characterization of distributions by conditional expectation of order statistics. J Appl Sci 9:159–168

38.

Malik HJ (1970) Estimation of the parameters of the Pareto distribution. Metrika 15:126–132CrossRef

39.

Miller RG Jr (1981) Simultaneous statistical inference, 2nd edn. Springer, New YorkCrossRef

40.

Pachner J (1984) Handbook of numerical analysis applications with programs for engineers and scientists. Mc Graw-Hill Inc., New York

41.

Pareto V (1897) Cours d’ economie politique. Rouge and Cie, Lausanne and Paris

42.

Rauhut BO (1982) Estimation of the mean of an Exponential distribution with an outlying observation. Commun Stat Theory Methods 11:1439–1452CrossRef

43.

Read RR (1981) Representation of certain covariance matrices with application to asymptotic efficiency. J Am Stat Assoc 76:148–154CrossRef

44.

Saksena Sk, Johnson AM (1984) Best unbiaesd estimators for the parameters of a two-parameter Pareto distribution. Metrika 31:77–83CrossRef

45.

Swain JJ, Venkatraman S, Wilson JR (1988) Least squares estimation of distribution function in Johnson’s translation system. J Stat Comput Simul 29(4):271–297CrossRef

46.

Veale JR (1975) Improved estimation of expected life when one identified suprious observation may be present. Am Stat Assoc 70:398–401CrossRef

Title: Estimation of the Lomax Distribution in the Presence of Outliers
Author: Mehdi Jabbari Nooghabi
Publication date: 15-09-2016
Publisher: Springer Berlin Heidelberg
Published in: Annals of Data Science / Issue 4/2016
Print ISSN: 2198-5804
Electronic ISSN: 2198-5812
DOI: https://doi.org/10.1007/s40745-016-0087-7

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