Some estimates of geometric sums

✍ Scribed by Jean-Louis Bon; Vladimir Kalashnikov

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 108 KB
• Volume: 55
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00136-5

✦ Synopsis

The paper is devoted to analysis of geometric convolutions emerging in various ÿelds of applied probability and, in particular, in reliability. The problem of bounding the distribution of such sums has been the subject of numerous works for last 20 years. Various bounds were proposed but their accuracy was sometimes not satisfactory for applications to highly reliable systems especially in the case of relatively small values of the time argument. Using truncation arguments, we propose new two-sided inequalities improving some known bounds.