Discussiones Mathematicae Probability and Statistics 25(2) (2005) 181-205

RECURRENCE RELATIONS FOR CONDITIONAL MOMENT GENERATING FUNCTIONS OF ORDER STATISTICS AND RECORD VALUES

Essam K. AL-Hussaini1, Abd EL-Baset A. Ahmad2 and Hanan H. El-Boghdady2

1Department of Statistics and O.R., Kuwait University, Kuwait
2Mathematics Department, Faculty of Science, University of Assiut, Egypt

Abstract

In this paper, recurrence relations for conditional moment generating functions and conditional moments of order statistics and record values based on random samples drawn from members of a class of doubly truncated distributions Ád are obtained.

Keywords: order statistics, record values, conditional moment generating functions, conditional moments, recurrence relations.

2000 Mathematics Subject Classification: Primary 62E10,Secondary 62G30.

References

[1] A.A. Ahmad and M.A. Fawzy, Recurrence relations for single moments of generalized order statistics from doubly truncated distributions, J. Statist. Plann. Inf. 117 (2003), 241-249.
[2] M. Ahsanullah, Record Statistics, Nova Science Publishers, Inc., Huntington 1995.
[3]M. Ahsanullah and V. Nevzorov, Ordered Random Variables, Nova Science Publishers, Inc., Huntington 2001.
[4]E.K. AL-Hussaini, Predicting observables from a general class of distributions, J. Statist. Plann. Inf. 79 (1999), 79-91.
[5]E.K. AL-Hussaini and A.A. Ahmad, On Bayesian interval prediction of future records, Test 12 (2003a), 79-99.
[6]E.K. AL-Hussaini and A.A. Ahmad, On Bayesian predictive distributions of generalized order statistics, Metrika 57 (2003b), 165-176.
[7]E.K. AL-Hussaini, A.A. Ahmad and H.H. El-Boghdady, Recurrence relations for moment generating functions of order statistics, Metron LXII (2004a), 85-99.
[8]E.K. AL-Hussaini, A.A. Ahmad and H.H. El-Boghdady, Recurrence relations for moment generating functions of record values, (2004b) submitted.
[9] E.K. AL-Hussaini and M.I. Osman, On the median of finite mixtures, J. Statist. Comput. Simul. 58 (1997), 121-144.
[10] B.C Arnold, N. Balakrishnan and H.N. Nagaraja, A First Course in Order Statistics, Wiley, New York 1992.
[11]B.C Arnold, N. Balakrishnan and H.N. Nagaraja, Records, Wiley, New York 1998.
[12]N. Balakrishnan and A.C. Cohen, Order Statistics Estimation Methods, Academic Press, Boston 1991.
[13]David, Order Statistics, First Edition, Wiley, New York 1970.
[14]David, Order Statistics, Second Edition, Wiley, New York 1981.
[15]H.L. Harter, Order Statistics and Their Use in Testing and Decision, U.S. Governmemt Printing Office, Washington D.C. (Vol. 1 and 2, 1970).
[16]J.S. Hwang and G.D. Lin, Extensions of Müntz Szàsz theorem and applications, Analysis 4 (1984), 143-160.
[17]R.D. Reiss, Approximate Distributions of Order Statistics with Applications to Nonparametric Statistics, Springer Verlag, Berlin 1989.
[18]A.E. Sarhan and B.G. Greenberg, Contributions to Order Statistics, (eds) Wiley, New York 1962.

Received 20 April 2004