Advertisement

Order Statistics from Independent Exponential Random Variables and the Sum of the Top Order Statistics

  • H. N. Nagaraja
Chapter
Part of the Statistics for Industry and Technology book series (SIT)

Abstract

Let X (1)<...<X (n) be the order statistics from n independent nonidentically distributed exponential random variables. We investigate the dependence structure of these order statistics, and provide a distributional identity that facilitates their simulation and the study of their moment properties. Next, we consider the partial sum T i=∑ j=i+1 n X (j), 0≥in−1. We obtain an explicit expression for the cdf of T i , exploiting the memoryless property of the exponential distribution. We do this for the identically distributed case as well, and compare the properties of T i under the two settings.

Keywords and phrases

Markov property equal in distribution simulation mixtures selection differential 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andrews, D. M. (1996). Moments of the selection differential from exponential and uniform parents, In Statistical Theory and Applications: Papers in Honor of Herbert A. David (Eds. H. N. Nagaraja, P. K. Sen, and D. F. Morrison), pp. 67–80, Springer-Verlag, New York.Google Scholar
  2. 2.
    Choi, Y.-S., Nagaraja, H. N., and Alamouti, S. M. (2003). Performance analysis and comparisons of antenna and beam selection/combining diversity, Submitted for publication.Google Scholar
  3. 3.
    David, H. A., and Nagaraja, H. N. (2003). Order Statistics, Third edition, John Wiley_& Sons, New York.zbMATHGoogle Scholar
  4. 4.
    Khaledi, B.-E., and Kochar, S. (2000). Dependence among spacings, Probability in the Engineering and Information Sciences, 14, 461–472.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Nagaraja, H. N. (1981). Some finite sample results for the selection differential, Annals of the Institute of Statistical Mathematics, 33, 437–448.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Nagaraja, H. N. (1982). Some nondegenerate limit laws for the selection differential, Annals of Statistics, 10, 1306–1310.zbMATHMathSciNetGoogle Scholar
  7. 7.
    Nevzorov, V. B. (1984). Representations of order statistics, based on exponential variables with different scaling parameters, Zapiksi Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta imeni V. A. Steklova Akademii Nauk SSSR (LOMI), 136, 162–164; English translation (1986). Journal of Soviet Mathematics, 33, 797–798.MathSciNetzbMATHGoogle Scholar
  8. 8.
    Nevzorova, L., and Nevzorov, V. (1999). Ordered random variables, Acta Applicandae Mathematicae, 58, 217–229.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Proschan, F., and Sethuraman, J. (1976). Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability, Journal of Multivariate Analysis, 6, 608–616.CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Rényi, A. (1953). On the theory of order statistics, Acta Mathematica Academiae Scientiarum Hungaricae, 4, 191–231.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Tikhov, M. (1991). Reducing of test duration for censored samples, Theory of Probability and Applications, 36, 604–607.MathSciNetCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • H. N. Nagaraja
    • 1
  1. 1.The Ohio State UniversityColumbusUSA

Personalised recommendations