Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T04:53:35.305Z Has data issue: false hasContentIssue false
  • English
  • Français

SOME UNIFIED RESULTS ON COMPARING LINEAR COMBINATIONS OF INDEPENDENT GAMMA RANDOM VARIABLES

Published online by Cambridge University Press:  08 June 2012

Subhash Kochar  and
Maochao Xu
Subhash Kochar
Affiliation:
Department of Mathematics and Statistics, Portland State University, Portland, OR
Maochao Xu
Affiliation:
Department of Mathematics, Illinois State University, Normal, IL E-mail: mxu2@ilstu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, a new sufficient condition for comparing linear combinations of independent gamma random variables according to star ordering is given. This unifies some of the newly proved results on this problem. Equivalent characterizations between various stochastic orders are established by utilizing the new condition. The main results in this paper generalize and unify several results in the literature including those of Amiri, Khaledi, and Samaniego [2], Zhao [18], and Kochar and Xu [9].

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 3 , July 2012 , pp. 393 - 404
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Ahmed, A.N., Alzaid, A., Bartoszewicz, J., & Kochar, S.C. (1986). Dispersive and superadditive ordering. Advances in Applied Probability 18: 1019–1022.CrossRefGoogle Scholar
2.Amiri, L., Khaledi, B.H., & Samaniego, F.J. (2011). On skewness and dispersion among convolutions of independent gamma random variables. Probability in the Engineering and Informational Sciences 25: 55–69.Google Scholar
3.Bagai, I. & Kochar, S. (1986). On tail ordering and comparison of failure rates. Communications in Statistics Theory and Methods 15: 1377–1388.CrossRefGoogle Scholar
4.Bock, M.E., Diaconis, P., Huffer, F.W., & Perlman, M.D. (1987). Inequalities for linear combinations of gamma random variables. The Canadian Journal of Statistics 15: 387–395.Google Scholar
5.Diaconis, P. & Perlman, M.D. (1987). Bounds for tail probabilities of linear combinations of independent gamma randomvariables. The symposium on dependence in statistics and probability, Hidden Valley, Pennsylvania.Google Scholar
6.Fernández-Ponce, J.M., Kochar, S.C., & Muñoz-Perez, J. (1998). Partial orderings of distributions based on right-spread functions. Journal of Applied Probability 35: 221–228.CrossRefGoogle Scholar
7.Khaledi, B.E. & Kochar, S. (2004). Ordering convolutions of gamma random variables. Sankhya 66: 466–473.Google Scholar
8.Kochar, S. & Xu, M. (2010). On the right spread order of convolutions of heterogeneous exponential random variables. Journal of Multivariate Analysis 101: 165–176.Google Scholar
9.Kochar, S. & Xu, M. (2011). The tail behavior of the convolutions of gamma random variables. Journal of Statistical Planning and Inferences 141: 418–428.CrossRefGoogle Scholar
10.Korwar, R.M. (2002). On stochastic orders for sums of independent random variables. Journal of Multivatiate Analysis 80: 344–357.Google Scholar
11.Marshall, A.W. & Olkin, I. (1979). Inequalities: theory of majorization and its applications. Academic Press, New York.Google Scholar
12.Marshall, A.W. & Olkin, I. (2007). Life Distributions. Springer, New York.Google Scholar
13.Mi, J., Shi, W., & Zhou, Y.Y. (2008). Some properties of convolutions of Pascal and Erlang random variables. Statistics and Probability Letters 78: 2378–2387.CrossRefGoogle Scholar
14.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders and their applications. New York: Springer.Google Scholar
15.Shaked, M. & Shantikumar, J.G. (1998). Two variability orders. Probability in the Engineering and Informational Sciences 12: 1–23.CrossRefGoogle Scholar
16.Sim, C.H. (1992). Point processes with correlated gamma interarrival times. Statistics and Probability Letters 15: 135–141.Google Scholar
17.Yu, Y. (2009). Stochastic ordering of exponential family distributions and their mixtures. Journal of Applied Probability 46: 244–254.Google Scholar
18.Zhao, P. (2011). Some new results on convolutions of heterogeneous gamma random variables. Journal of Multivariate Analysis 102: 958–976.CrossRefGoogle Scholar
19.Zhao, P. & Balakrishnan, N. (2010). Mean residual life order of convolutions of heterogenous exponential random variables. Journal of Multivariate Analysis 100: 1792–1801.CrossRefGoogle Scholar