Abstract. In his paper we consider the associated claim size distribution arising in the risk model with random premium income. We derive conditions under which the aging properties of loss distribution are preserved for the associated claim size distribution. The ordering relationships between the associated claim size distribution and loss distribution for the failure rate function and mean residual lifetime are also investigated.

Received: May 13, 2013

AMS Subject Classification: 62P05, 91B30

Key Words and Phrases: associated claim size distribution, failure rate function, mean residual lifetime

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