Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T10:32:13.008Z Has data issue: false hasContentIssue false
  • English
  • Français

Some monotonicity properties of the delayed renewal function

Published online by Cambridge University Press:  14 July 2016

B. G. Hansen  and
J. B. G. Frenk
B. G. Hansen
Affiliation:
Georg-August-University, Göttingen
J. B. G. Frenk*
Affiliation:
Erasmus University, Rotterdam
*
∗∗ Postal address: Econometric Institute, Erasmus University, P.O. Box 1738, NL-3000 DR Rotterdam, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

Analogues of some theorems of Brown (1980) concerning renewal measures with DFR or IMRL underlying distributions are proved for delayed renewal measures. Some related results, such as partial converses of the main theorems, are also presented.

Keywords

DFRIMRNWULOG-CONVEX
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 811 - 821
Copyright
Copyright © Applied Probability Trust 1991 

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.)

Footnotes

∗

Present address: Commission of the European Communities, JRC Ispra Establishment, Inst, for the Environment, Envir. Chem./Life Sci. Division, 1–21020 Ispra (Varese), Italy.

References

Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Brown, M. (1980) Bounds, inequalities and monotonicity properties for some specialized renewal processes. Ann. Prob. 8, 227–240.Google Scholar
Brown, M. (1981) Further monotonicity properties for specialized renewal processes. Ann. Prob. 9, 891–895.Google Scholar
Bruijn, N. G. De and Erdös, P. (1953) On a recursion formula and some Tauberian theorems. J. Research Nat. Bureau Stand. 50, 161–164.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and Its Applications, Vol. I, 3rd. edn. Wiley, New York.Google Scholar
Feller, W. (1972) An Introduction to Probability Theory and Its Applications, Vol. II, 2nd. edn. Wiley, New York.Google Scholar
Hansen, B. G. (1988) On logconcave and logconvex infinitely divisible sequences and densities. Ann. Prob. 16, 1832–1839.Google Scholar
Kaluza, T. (1928) über die Koeffizienten Reziproks Potenzreihen. Math. Z. 28, 161–170.Google Scholar
Kingman, J. F. C. (1972) Regenerative Phenomena. Wiley, London.Google Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Shanthikumar, J. G. (1988) DFR property of first-passage times and its preservation under geometric compounding. Ann. Prob. 16, 397–406.Google Scholar