By by Bjørn Sundt.
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Extra info for An introduction to non-life insurance mathematics
A similar hierarchical extension of the credibility regression model of Section 6. 7 is described by Sundt (1979b). 8E. 8 it should be obvious how to treat hierarchies with more levels. g. assume that data from different communities in the same county are conditionally independent given an unknown random (t>O; 0>0) a) Find the conditional expectation of T-t given that T>t. Comment on this result. The parameter 0 depends on the quality of the glow thread and does not have the same value for all bulbs.
Xn of the same dimension are exchangeable relative to a random vector Y if Xi ,... ,Xi ,Y have the same joint distrin 1 bution for all permutations (i ,... ,in) of (1, ... ,n). 1 Show that if X1' ... ,Xn are exchangeable relative to (M,X ), then (X ,X) with 0 0 1 X= nXjis linearly sufficient for Mbased on (X ,xl'" .. ,Xn). 1 1::; 0 The concept of relative exchangeability was introduced in Sundt (1979a), where the result of this exercise was also proved. A different proof was given in Sundt (1991a).
We also mentioned engine power as a technical variable; a more powerful car could be driven at higher speed and could therefore be more exposed to accidents. From this one should not conclude that a more powerful car in itself is more dangerous than a less powerful car. A person who considers buying a new car, should not necessarily conclude that it is safer for him to buy a less powerful car as a more powerful car would be more dangerous to him; perhaps it could actually be the opposite as with the more powerful car he would have the power available when he needs it.
An introduction to non-life insurance mathematics by by Bjørn Sundt.