On the DFR property of the compound geometric distribution with applications in risk theory

Georgios Psarrakos

Insurance: Mathematics and Economics, 2010, vol. 47, issue 3, 428-433

Abstract: In 1988, Shanthikumar proved that the sum of a geometrically distributed number of i.i.d. DFR random variables is also DFR. In this paper, motivated by the inverse problem, we study monotonicity properties related to defective renewal equations, and obtain that if a compound geometric distribution is DFR, then the random variables of the sums are NWU (a class that contains DFR). Furthermore, we investigate some applications of risk theory and give a characterization of the exponential distribution.

Keywords: Compound; geometric; distribution; Renewal; equation; DFR; (IFR); NWU; (NBU); IMRL; (DMRL); NWUE; (NBUE); Ladder; height; Ruin; probability (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:47:y:2010:i:3:p:428-433

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