Parameter Risk

[actuarymath 1]

I believe that how few we consider the "parameter risk".Suppose that the probability of occurring a accident is P (0<P<1).For N polices, the probability of occurring n accidents isN_C_n * P^n * (1-P)^(N-n)(where N_C_n means the combinatorial number which is chosen n things form N things)Suppose that the p.d.f.(probability density function) of the prior distribution is g(p),f(p),the p.d.f. of the posterior distribution by Bayes' theoremwill be proportional to P^n * (1-P)^(N-n) *g(p)(because N_C_n is a constant which has no relations with p)Now if the prior distribution is a uniform distribution, that is g(p)=1(0<p<1)f(p) is proportional to P^n*(1-P)^(N-n)soP follows to B(n+1,N+1)(beta distribution).