The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, we show that the proportional hazard rates (PHR) model, which includes some well-known...

The usual credibility formula holds whenever, (i) claim size distribution is a member of the exponential family of distributions, (ii) prior distribution conjugates with claim size distribution, and (iii) square error loss has been considered. As long as, one of these conditions is violent, the...

Payandeh [Payandeh Najafabadi, A.T., 2010. A new approach to credibility formula. Insurance: Mathematics and Economy 46, 334–338] introduced a new technique to approximate a Bayes’ estimator with the exact credibility’s form. This article employs a well known and powerful maximum-entropy...