Moments of order statistics of the Generalized T Distribution
Discussiones Mathematicae. Probability and Statistics, Tome 35 (2015) no. 1-2, pp. 95-106.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: best linear unbiased estimates, generalized Kampé de Fériet, function, generalized t (GT) distribution, moments of order statistics
@article{DMPS_2015_35_1-2_a6,
     author = {Gen\c{c}, Ali},
     title = {Moments of order statistics of the {Generalized} {T} {Distribution}},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {95--106},
     publisher = {mathdoc},
     volume = {35},
     number = {1-2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2015_35_1-2_a6/}
}
TY  - JOUR
AU  - Genç, Ali
TI  - Moments of order statistics of the Generalized T Distribution
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2015
SP  - 95
EP  - 106
VL  - 35
IS  - 1-2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2015_35_1-2_a6/
LA  - en
ID  - DMPS_2015_35_1-2_a6
ER  - 
%0 Journal Article
%A Genç, Ali
%T Moments of order statistics of the Generalized T Distribution
%J Discussiones Mathematicae. Probability and Statistics
%D 2015
%P 95-106
%V 35
%N 1-2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2015_35_1-2_a6/
%G en
%F DMPS_2015_35_1-2_a6
Genç, Ali. Moments of order statistics of the Generalized T Distribution. Discussiones Mathematicae. Probability and Statistics, Tome 35 (2015) no. 1-2, pp. 95-106. http://geodesic.mathdoc.fr/item/DMPS_2015_35_1-2_a6/

[1] B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, A First Course in Order Statistics (Wiley, New York, 1992).

[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.

[3] O. Arslan, Family of multivariate generalized t distributions, Journal of Multivariate Analysis 89 (2004), 329-337.

[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.

[5] H.A. David and H.N. Nagaraja, Order Statistics (Wiley, Hoboken, New Jersey, 2003).

[6] H. Exton, Multiple Hypergeometric Functions (Halstead, New York, 1976).

[7] H. Exton, Handbook of Hypergeometric Integrals: Theory Applications, Tables, Computer Programs (Halsted Press, New York, 1978).

[8] T. Fung and E. Seneta, Extending the multivariate generalised t and generalised VG distributions, Journal of Multivariate Analysis 101 (2010), 154-164.

[9] A.İ. Genç, The generalized T Birnbaum–-Saunders family, Statistics 47 (2013), 613-625.

[10] P.W. Karlsson, Reduction of certain generalized Kampé de Fériet functions, Math. Scand. 32 (1973), 265-268.

[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.

[12] S. Nadarajah, Explicit expressions for moments of t order statistics, C.R. Acad. Sci. Paris, Ser. I. 345 (2007), 523-526.

[13] S. Nadarajah, On the generalized t (GT) distribution, Statistics 42 (2008a), 467-473.

[14] S. Nadarajah, Explicit expressions for moments of order statistics, Statistics and Probability Letters 78 (2008b), 196-205.

[15] B. Rosner, On the detection of many outliers, Technometrics 17 (1975), 221-227.

[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.

[17] H.D. Vu, Iterative algorithms for data reconciliation estimator using generalized t-distribution noise model, Ind. Eng. Chem. Res. 53 (2014), 1478-1488.

[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.

[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.

[20] W. Research, Inc.,Mathematica, Version 9.0 Champaign, IL (2012).