EXPLOITING THE WAITING TIME PARADOX: APPLICATIONS OF THE SIZE-BIASING TRANSFORMATION
- 1 January 2006
- journal article
- research article
- Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences
- Vol. 20 (2) , 195-230
- https://doi.org/10.1017/s026996480606013x
Abstract
We consider the transformation T that takes a distribution F into the distribution of the length of the interval covering a fixed point in the stationary renewal process corresponding to F. This transformation has been referred to as size-biasing, length-biasing, the renewal length transformation, and the stationary lifetime operator. We review and develop properties of this transformation and apply it to diverse areas.Keywords
This publication has 9 references indexed in Scilit:
- Interlacing Eigenvalues in Time Reversible Markov ChainsMathematics of Operations Research, 1999
- Tree-valued Markov chains derived from Galton-Watson processesAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, 1998
- Size-biased and conditioned random splitting treesStochastic Processes and their Applications, 1996
- Strong Stationary Times Via a New Form of DualityThe Annals of Probability, 1990
- Tight Bounds on the Exponential Approximation of Some Aging DistributionsThe Annals of Probability, 1988
- A Natural Identity for Exponential Families with Applications in Multiparameter EstimationThe Annals of Statistics, 1978
- Convergence of a sequence of transformations of distribution functionsPacific Journal of Mathematics, 1969
- Bounds for Distributions with Monotone Hazard Rate, IIThe Annals of Mathematical Statistics, 1964
- An Inversion Formula for Laplace Transforms and Semi-Groups of Linear OperatorsAnnals of Mathematics, 1954