Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-25T10:51:22.987Z Has data issue: false hasContentIssue false
  • English
  • Français

A Characterization of the Compound-Exponential Type Distributions

Published online by Cambridge University Press:  20 November 2018

Tea-Yuan Hwang  and
Chin-Yuan Hu
Tea-Yuan Hwang
Affiliation:
Graduate School of Mathematical Sciences, Aletheia University, Tamsui Taipei 25103, Taiwan, ROC e-mail: Hwang@stat.nthu.edu.tw
Chin-Yuan Hu
Affiliation:
Department of Business Education, National Changhua University of Education, Changhua 50058, Taiwan, ROC e-mail: buhuua@cc.ncue.edu.tw
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, a fixed point equation of the compound-exponential type distributions is derived, and under some regular conditions, both the existence and uniqueness of this fixed point equation are investigated. A question posed by Pitman and Yor can be partially answered by using our approach.

Keywords

62E1060G50fixed point equationcompound-exponential type distributions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 3 , 01 September 2011 , pp. 464 - 471
Copyright
Copyright © Canadian Mathematical Society 2011

References

[1] Eckberg, A. E. Jr., Sharp bounds on Laplace-Stieltjes transforms, with applications to various queueing problems. Math. Oper. Res. 2(1977), no. 2, 135–142. doi:10.1287/moor.2.2.135Google Scholar
[2] Feller, W., An Introduction to Probability Theory and Its Applications. Vol. 2. Second edition. John Wiley & Sons, New York, 1971.Google Scholar
[3] GuljaŠ, B., Pearce, C. E. M., and Pečarić, J., Jensen's inequality for distributions possessing higher moments, with application to sharp bounds for Laplace-Stieltjes transforms. J. Austral. Math. Soc. Ser. B 40(1998), no. 1, 80–85. doi:10.1017/S0334270000012388Google Scholar
[4] Hu, C.-Y. and Lin, G. D, Some inequalities for Laplace transforms. J. Math. Anal. Appl. 340(2008), no. 1, 675–686. doi:10.1016/j.jmaa.2007.08.031Google Scholar
[5] Iksanov, A. M. and Kim, C. S., On a Pitman-Yor problem. Statis. Probab. Lett. 68(2004), no. 1, 61–72. doi:10.1016/j.spl.2004.01.015Google Scholar
[6] Iksanov, A. M. and Kim, C. S., New explicit examples of fixed points of Poisson shot noise transforms. Aust. N. Z. T. Stat. 46(2004), no. 2, 313–321. doi:10.1111/j.1467-842X.2004.00332.xGoogle Scholar
[7] Pakes, A. G., On characterizations through mixed sums. Austral. J. Statist. 34(1992), no. 2, 323–339. doi:10.1111/j.1467-842X.1992.tb01364.xGoogle Scholar
[8] Pitman, J. and Yor, M., Infinitely divisible laws associated with hyperbolic functions. Canad. J. Math. 55(2003), no. 2, 292–330. doi:10.4153/CJM-2003-014-xGoogle Scholar
[9] Sen, A. and Khattree, R., Length biased distribution, equilibrium distribution and characterization of probability laws. J. Appl. Statist. Sci. 3 1996, no. 4, 239–252.Google Scholar
[10] Steutel, F. W. and Harn, K. van, Infinite Divisibility of Probability Distributions on the Real Line. Monographs and Textbooks in Pure and Applied Mathematics 259. Marcel Dekker, New York, 2004.Google Scholar