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Total positivity and renewal theory. (English) Zbl 0682.60078
Probability, statistics, and mathematics, Pap. in Honor of Samuel Karlin, 141-162 (1989).
[For the entire collection see Zbl 0679.00013.]
The paper unifies and considerably extends several known results on the relations between a probability density f and the corresponding renewal density u by means of total positivity. Moreover for a density f with decreasing failure rate there is given a straight forward proof of the fact that (in the discrete time formulation) $$u(n)-u(n+1)$$ is asymptotic to a constant multiple of the tail probabilities of f.
Reviewer: M.Schäl

##### MSC:
 60K05 Renewal theory
##### Keywords:
renewal density; total positivity; tail probabilities