We derive an explicit expression for the single moments of order statistics from the generalized t (GT) distribution. We also derive an expression for the product moment of any two order statistics from the same distribution. Then the location-scale estimating problem of a real data set is solved alternatively by the best linear unbiased estimates which are based on the moments of order statistics.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1174,
author = {Ali \.I. Gen\c c},
title = {Moments of order statistics of the Generalized T Distribution},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {35},
year = {2015},
pages = {95-106},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1174}
}
Ali İ. Genç. Moments of order statistics of the Generalized T Distribution. Discussiones Mathematicae Probability and Statistics, Tome 35 (2015) pp. 95-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1174/
[000] [1] B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, A First Course in Order Statistics (Wiley, New York, 1992). | Zbl 0850.62008
[001] [2] O. Arslan and A.İ. Genç, Robust location and scale estimation based on the univariate generalized t (GT) distribution, Commun. Stat.-Theor. Methods 32 (2003), 1505-1525. | Zbl 1184.62024
[002] [3] O. Arslan, Family of multivariate generalized t distributions, Journal of Multivariate Analysis 89 (2004), 329-337. | Zbl 1049.62058
[003] [4] S.T.B. Choy and J.S.K Chan, Scale mixtures distributions in statistical modelling, Aust. N.Z.J. Stat. 50 (2008), 135-146. | Zbl 1145.62006
[004] [5] H.A. David and H.N. Nagaraja, Order Statistics (Wiley, Hoboken, New Jersey, 2003). | Zbl 1053.62060
[005] [6] H. Exton, Multiple Hypergeometric Functions (Halstead, New York, 1976).
[006] [7] H. Exton, Handbook of Hypergeometric Integrals: Theory Applications, Tables, Computer Programs (Halsted Press, New York, 1978).
[007] [8] T. Fung and E. Seneta, Extending the multivariate generalised t and generalised VG distributions, Journal of Multivariate Analysis 101 (2010), 154-164. | Zbl 1182.62121
[008] [9] A.İ. Genç, The generalized T Birnbaum–-Saunders family, Statistics 47 (2013), 613-625. | Zbl 1327.60039
[009] [10] P.W. Karlsson, Reduction of certain generalized Kampé de Fériet functions, Math. Scand. 32 (1973), 265-268. | Zbl 0268.33006
[010] [11] J.B. McDonald and W.K. Newey, Partially adaptive estimation of regression models via the generalized t distribution, Econ. Theor. 4 (1988), 428-457.
[011] [12] S. Nadarajah, Explicit expressions for moments of t order statistics, C.R. Acad. Sci. Paris, Ser. I. 345 (2007), 523-526. | Zbl 1124.62033
[012] [13] S. Nadarajah, On the generalized t (GT) distribution, Statistics 42 (2008a), 467-473. | Zbl 1274.62123
[013] [14] S. Nadarajah, Explicit expressions for moments of order statistics, Statistics and Probability Letters 78 (2008b), 196-205. | Zbl 1290.62023
[014] [15] B. Rosner, On the detection of many outliers, Technometrics 17 (1975), 221-227. | Zbl 0308.62025
[015] [16] D.C. Vaughan, The exact values of the expected values, variances and covariances of the order statistics from the Cauchy distribution, J. Statist. Comput. Simul. 49 (1994), 21-32. | Zbl 0846.62014
[016] [17] H.D. Vu, Iterative algorithms for data reconciliation estimator using generalized t-distribution noise model, Ind. Eng. Chem. Res. 53 (2014), 1478-1488.
[017] [18] D. Wang and J.A. Romagnoli, Generalized t distribution and its applications to process data reconciliation and process monitoring, Transactions of the Institute of Measurement and Control 27 (2005), 367-390.
[018] [19] J.J.J. Wang, S.T.B. Choy and J.S.K. Chan, Modelling stochastic volatility using generalized t distribution, Journal of Statistical Computation and Simulation 83 (2013), 340-354. | Zbl 06170048
[019] [20] W. Research, Inc.,Mathematica, Version 9.0 Champaign, IL (2012).