Student Solutions Manual to Accompany Loss Models: From Data to Decisions by Klugman Stuart A.;Panjer Harry H.;Willmot Gordon E.; & Harry H. Panjer & Gordon E. Willmot

Author:Klugman, Stuart A.;Panjer, Harry H.;Willmot, Gordon E.; & Harry H. Panjer & Gordon E. Willmot
Language: eng
Format: epub
Publisher: John Wiley & Sons, Inc.
Published: 2019-12-17T00:00:00+00:00

11.44 The loglikelihood function is . Also, and . Using , we have

and its inverse is

The mean is , and so the derivative vector is . The variance of is estimated as 227,763 and a 95% CI is .

11.45 . . . . . Inserting the estimate gives 2.9844.

Evaluated at , it is 239.88. The derivative with respect to is

which is − 39.428 when evaluated at . The variance of the LEV estimator is , and the CI is .

Section 11.7

11.46 The likelihood function is . Then . With , . A 95% confidence region solves . The solutions are 946.87 and 2,285.07. Inserting the solutions in produces the interval 0.810 to 0.916. The symmetric interval was 0.816 to 0.922.

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