Abstract
Results of Jain and Khan (1979) and Khan and Jain (1978) on the time to first emptiness of a reservoir are generalized to include the case of defective random variables where the mass at ∞ can be positive. The assumption of an underlying exponential family is not needed — the general condition is infinite divisibility and closure under convolutions. The support of the distributions can be nonnegative reals or nonnegative integers. Examples are given to illustrate the general theory and show the bivariate extension.
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