By by Bjørn Sundt.
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Additional info for An introduction to non-life insurance mathematics
Show that the conditi- Pr( Y=l) = 1- Pr( Y=O) = v. andK-=Ifi/A. Comment. 14 The log-normal distribution is often used as a distribution for claim amounts. We say that a random variable X is log-normally distributed with parameters p, and a if In X is normally distributed with mean p, and standard deviation a. a) Find expressions for the density, mean, and variance of the log-normal distribution with parameters p, and a. Let X1,X2,... be conditionally independent and identically log-normally distributed with parameters e and a given a random variable e which is normally distributed with mean 1J and standard deviation r.
Let r( 0) be a real-valued vector function of 0 and r an estimator -52- . -53- . of r(9). s. 7. The best linear 9-unbiased estimator ofb(9) based on X is b. Proof It is clear that the coefficients of the best linear 9-unbiased estimator of b(e) depends on at most first and second order unconditional moments of (X' ,b(9)')'. Thus it is sufficient to prove the result for a special case with the same first and second order moments as the general case. We therefore make, without loss of generality, the additional assumption that Cov[XI 9]=~ independent of e.
P .. = E. X .. ZJ ZJ J== 1 ZJ I I E. P .. = E. X Z= 1 ZJ ZJ Z=1 ij ( i=1, ... ,1) (j=1, ... 2) as ( i=1, ... ,1) (j=1, ... ,J) Often one does not want to adjust the parameters for all the rating factors in a revision of rates. If we only want to adjust the parameters for factors l, ... 2) for k=l, ... ,L. We see that the method of marginal totals does not impose any structure on the parameters to be determined. Thus, the method can produce results that could seem unreasonable to insurance agents and policyholders.
An introduction to non-life insurance mathematics by by Bjørn Sundt.