an:04117608
Zbl 0682.60078
Liggett, Thomas M.
Total positivity and renewal theory
EN
Probability, statistics, and mathematics, Pap. in Honor of Samuel Karlin, 141-162 (1989).
1989
a
60K05
renewal density; total positivity; tail probabilities
[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.
M.Sch??l
Zbl 0679.00013