Research ArticleOpen AccessGoogle Scholar indexed
Best Equivariant Estimator of Extreme Quantiles in the Multivariate Lomax Distribution
Department of Statistics, College of Mathematical Sciences, Alzahra University, Tehran, Iran
- 1 Department of Statistics, College of Mathematical Sciences, Alzahra University, Tehran, Iran
Open Journal of Statistics·Volume 05 (2015)·Pages 350–354·Published 22 May 2015·DOI10.4236/ojs.2015.54036
Copy link · social · email
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.
KeywordsBest Affine Equivariant EstimatorQuantile EstimationLomax (Pareto II) DistributionsLinex Loss Function
- 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
- Bryson, M. (1974) Heavy-Tailed Distributions: Properties and Tests. Technometrics, 16, 61-68. http://dx.doi.org/10.1080/00401706.1974.10489150
- Arnold, B. (1983) Pareto Distribution. International Cooperative Publishing House, Silver Spring Maryland.
- Johnson, N., Kotz, S. and Balakrishnan, N. (1994) Continous Univariate Distributions. Vol. 1, 2nd Edition, Wiley & Sons, New York.
- 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
- 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
- Kotz, S., Balakrishnan, N. and Johnson, N.L. (2000) Continuous Multivariate Distributions, Vol. 1, Models and Applications, 2nd Edition, Wiley & Sons, New York.
- 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
- 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
- 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
- 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.
- 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
- 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