Loss sizes follow a lognormal distribution. You have estimated the parameters of the distribution as mu=3 and sigma = 0.5. The information matrix is
(200 0
0 400)
You estimate the mean of the lognormal distribution using the estimated parameters. Approximate the asymptotic variance of the estimate of the mean using the delta method.
Answer: Var(mu^) = 1/200, Var(sigma^)= 1/400
dg/du = e^(mu + sig squared/2) = 22.7599
dg/dsig = sige^(mu +sig squared/2) = 11.3799
1/200(22.9599^2) + 1/400(11.3799)^2 = 2.9138
(200 0
0 400)
You estimate the mean of the lognormal distribution using the estimated parameters. Approximate the asymptotic variance of the estimate of the mean using the delta method.
Answer: Var(mu^) = 1/200, Var(sigma^)= 1/400
dg/du = e^(mu + sig squared/2) = 22.7599
dg/dsig = sige^(mu +sig squared/2) = 11.3799
1/200(22.9599^2) + 1/400(11.3799)^2 = 2.9138
ASM PE1 #17