SOME NEW BOUNDS FOR THE RENEWAL FUNCTION
| Autor: | Markos V. Koutras, Konstadinos Politis |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Statistics and Probability
Class (set theory) Distribution (number theory) Management Science and Operations Research Type (model theory) Lifetime distribution Upper and lower bounds Industrial and Manufacturing Engineering Combinatorics Renewal function Monotone polygon Interval (graph theory) Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Probability in the Engineering and Informational Sciences. 20:231-250 |
| ISSN: | 1469-8951 0269-9648 |
| Popis: | In the literature, most of the bounds for the renewal function U(x) corresponding to a lifetime distribution F are given in terms of the first two moments of F only. The best general upper bound of this type is the one given in Lorden (1970). In the present article, we show that improved bounds can be obtained if one exploits the specific form of the distribution F. We derive a bound that improves upon Lorden's, at least on an interval [0,a) with a ≤ ∞, and we give both sufficient and necessary conditions for this improvement to hold uniformly for x ≥ 0. Refined upper as well as lower bounds are given for the case where F belongs to a class of distributions with monotone aging or when the renewal density is monotone. |
| Databáze: | OpenAIRE |
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