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

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.

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