Best Equivariant Estimator of Extreme Quantiles in the Multivariate Lomax Distribution

N. Sanjari Farsipour

doi:10.4236/ojs.2015.54036

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Best Equivariant Estimator of Extreme Quantiles in the Multivariate Lomax Distribution

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DOI: 10.4236/ojs.2015.54036 1,939 Downloads 2,304 Views

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N. Sanjari Farsipour

Affiliation(s)

Department of Statistics, College of Mathematical Sciences, Alzahra University, Tehran, Iran.

ABSTRACT

The minimum risk equivariant estimator of a quantile of the common marginal distribution in a multivariate Lomax distribution with unknown location and scale parameters under Linex loss function is considered.

KEYWORDS

Best Affine Equivariant Estimator, Quantile Estimation, Lomax (Pareto II) Distributions, Linex Loss Function

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Sanjari Farsipour, N. (2015) Best Equivariant Estimator of Extreme Quantiles in the Multivariate Lomax Distribution. Open Journal of Statistics, 5, 350-354. doi: 10.4236/ojs.2015.54036.

References

[1]	Lomax, K. (1954) Business Failures: Another Example of the Analysis of Failure Data. Journal of the American Statistical Association, 94, 847-852. http://dx.doi.org/10.1080/01621459.1954.10501239

[2]	Bryson, M. (1974) Heavy-Tailed Distributions: Properties and Tests. Technometrics, 16, 61-68. http://dx.doi.org/10.1080/00401706.1974.10489150

[3]	Arnold, B. (1983) Pareto Distribution. International Cooperative Publishing House, Silver Spring Maryland.

[4]	Johnson, N., Kotz, S. and Balakrishnan, N. (1994) Continous Univariate Distributions. Vol. 1, 2nd Edition, Wiley & Sons, New York.

[5]	Lindley, D. and Singpurwalla, N (1986) Multivariate Distributions for the Life Lengths of Components of a System Sharing a Common Environment. Journal of Applied Probability, 23, 418-431. http://dx.doi.org/10.2307/3214184

[6]	Nayak, Tk. (1987) Multivariate Lomax Distribution: Properties and Usefulness in Reliability Theory. Journal of Applied Probability, 24, 170-177. http://dx.doi.org/10.2307/3214068

[7]	Kotz, S., Balakrishnan, N. and Johnson, N.L. (2000) Continuous Multivariate Distributions, Vol. 1, Models and Applications, 2nd Edition, Wiley & Sons, New York.

[8]	Petropoulos, C. and Kourouklis, S. (2004) Improved Estimation of Extreme Quantiles in the Multivariate Lomax (Pareto II) Distribution. Metrika, 60, 15-24. http://dx.doi.org/10.1007/s001840300293

[9]	Petropoulos, C. and Kourouklis, S. (2001) Estimation of an Exponential Quantile under a General Loss and an Alternative Estimator under Quadratic Loss. Annals of the Institute of Statistical Mathematics, 53, 746-759. http://dx.doi.org/10.1023/A:1014648819462

[10]	Rukhin A. and Strawderman, W. (1982) Estimating a Quantile of an Exponential Distribution. Journal of the American Statistical Association, 77, 159-162. http://dx.doi.org/10.1080/01621459.1982.10477780

[11]	Varian, H.R. (1975) A Bayesian Approach to Real Estat Assessment. In: Fienberg, S.E. and Zellner, A., Eds., Studies in Bayesian Econometric and Statistics: In Honor of Leonard J. Savage, North Holland, Amesterdam, 195-208.

[12]	Zellner, A. (1986) Bayesian Estimation and Prediction Using Asymmetric Loss Function. Journal of American Statistical Association, 81, 446-451. http://dx.doi.org/10.1080/01621459.1986.10478289

[13]	Stein, C. (1964) Inadmissibility of the Usual Estimator for the Variance of a Normal Distribution with Unknown Mean. Annals of the Institute of Statistical Mathematics, 16, 155-160. http://dx.doi.org/10.1007/BF02868569

[14]	Brewster, J.F. and Zidek, J.V. (1974) Improving on Equivariant Estimators. Annals of Statistics, 2, 21-38. http://dx.doi.org/10.1214/aos/1176342610