Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T02:19:36.630Z Has data issue: false hasContentIssue false

Some inequalities on the distribution of ladder epochs

Published online by Cambridge University Press:  14 July 2016

D.Y. Downham*
Affiliation:
University of Liverpool
S.B. Fotopoulos*
Affiliation:
University of Liverpool
*
Postal address: Department of Computational and Statistical Science, The University of Liverpool, Victoria Building, Brownlow Hill, P.O. Box 147, Liverpool L69 3BX.
Postal address: Department of Computational and Statistical Science, The University of Liverpool, Victoria Building, Brownlow Hill, P.O. Box 147, Liverpool L69 3BX.

Abstract

An algorithm for calculating the probability distribution of ladder epochs is derived. Two theorems are given for bounds on the distribution function of ladder epoch probabilities.

Keywords

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 

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

Bhansali, R. J. and Downham, D. Y. (1977) Some properties of the order of an autoregressive model selected by a generalization of Akaike's FPE criterion. Biometrika 64, 547551.Google Scholar
Feller, W. (1970) An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. Wiley, London.Google Scholar
Iglehart, D. L. (1974) Random walks with negative drift conditioned to stay positive. J. Appl. Prob. 11, 742751.Google Scholar
Kleinrock, L. (1975) Queueing Systems, Vol. I. Wiley, London.Google Scholar
Veraverbeke, N. and Teugels, J. L. (1976) The exponential rate of convergence of the distribution of the maximum of a random walk. Part II J. Appl. Prob. 13, 733740.Google Scholar
Wald, A. (1947) Sequential Analysis. Wiley, New York.Google Scholar