Suppose Yı, Y2, ..., Yn represent the insurance claimant amounts that exceed 50 British pounds from n independent polici

[answerhappygod]

Suppose Yi Y2 Yn Represent The Insurance Claimant Amounts That Exceed 50 British Pounds From N Independent Polici 1 (102.09 KiB) Viewed 70 times

Suppose Yı, Y2, ..., Yn represent the insurance claimant amounts that exceed 50 British pounds from n independent policies under a kind of excess scheme, which are modelled by log(Y; – 50) ~ N(4,6), i = 1, 2, ..., n, where log stands for a base e logarithmic function. = = (a) Find the probability density function (pdf) of Yj; [6 marks] (b) Write down the likelihood function of 0 = (u, o-) based on Yı, Y2, , Yn, and find the maximum likelihood estimator (MLE) of 0 = (0,0%); [8 marks] (c) Find the score vector of O (u,02); [4 marks] (d) Find the Fisher information matrix of 0 = (u, o2); [5 marks] (e) Let Zi log(Y; 50). Write down the likelihood function of 0 = (u, 02) based on 21, 22, ..., Zn, and show that the MLE of (u, 04) based on Z1, Z2, ..., Zn is the same as the MLE of 0 = (0,0%) in Part (b). [7 marks] - -