6 An insurance company is trying to fit a paralogistic distr

6. An insurance company is trying to fit a paralogistic distribution to its claims data. The survival function for this distribution is given by S (x) = (1/1+(x/theta)^a)^a It is very important for the insurance company to correctly model the expected value and the 95th percentile of this distribution. The company therefore chooses alpha and Theta so that these values match their observed mean of 2.300 and their observed 95th percentile of 6,700. Which of the following values should they choose for a, and what should be the corresponding value of theta ? (i) 1.2131 (ii) 1.3871 (iii) 1.8786 (iv) 2.4322

Solution

Correct answer is (ii) 1.3871