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EXPLOITING THE WAITING TIME PARADOX: APPLICATIONS OF THE SIZE-BIASING TRANSFORMATION

Published online by Cambridge University Press:  06 March 2006

Mark Brown
Mark Brown
Affiliation:
Department of Mathematics, The City College, CUNY, New York, NY, E-mail: [email protected]
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 2 , April 2006 , pp. 195 - 230
Copyright
© 2006 Cambridge University Press

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