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Unformatted text preview: Credibility I ActSCi 432/832 1 / 16 Distributions Summary X is Binomial with parameters n (positive integer) and p (0 , 1) p . f . f ( x ) = n x p x (1 p ) n x for x = 0 , 1 , 2 , 3 ,...... n E ( X ) = np , Var ( X ) = np (1 p ) X is Bernoulli with parameters p (0 , 1) X is Binomial with n = 1 X is Poisson with parameter > p . f . f ( x ) = x e x ! for x = 0 , 1 , 2 , 3 ,...... E ( X ) = , Var ( X ) = 2 / 16 Distributions Summary X is Gamma with parameters > and > p . f . f ( x ) = x  1 e x / ( ) for x > E ( X k ) = k ( + k ) ( ) , if k > Note that ( + 1) = ( ) for > and ( + 1) = ! for = 0 , 1 , 2 ,.... X is Exponential with parameters > X is Gamma with = 1 X is Pareto with parameters > 0 and > p . f . f ( x ) = ( x + ) +1 for x > E ( X ) =  1 for > 1 , Var ( X ) = 2 (  1) 2 (  2) for > 2 3 / 16 Introduction Suppose a new policyholder has a risk say a fleet of cars to insure. Insurer will look up standard rates and charge, say, M per unit of risk. This the the manual premium as it comes from the handbook or manual. After a few years, the experience of the individual risk is available, which is X . Now the true premium is E ( X ) which is to be estimated from M or X . Which one is a better indicator of E ( X )? 4 / 16 The credibility theory is to take into account both information in a weighted average form: P = Z X + (1 Z ) M P is the credibility estimate of E ( X ) Z , 0 Z 1, is the credibility factor and measures the...
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This note was uploaded on 02/08/2012 for the course ACTSC 432 taught by Professor Davidlandriault during the Fall '09 term at Waterloo.
 Fall '09
 davidlandriault

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