Exploiting The Waiting Time Paradox: Applications Of The Size-Biasing Transformation

Authors:
Mark Brown
Affiliations:
Department of Mathematics, The City College, CUNY, New York, NY, E-mail: CYBERGARF@aol.com
Venue:
Probability in the Engineering and Informational Sciences
Year:
2006

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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.