An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 12.5, Problem 1Q
To determine
An appropriate data transformation and do the indicated analysis of variance.
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Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
Chapter 12 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 12.2 - Prob. 1QCh. 12.2 - Mount Etna erupted in 1669, 1780, and 1865 (recall...Ch. 12.2 - An indicator of the value of a stock relative to...Ch. 12.2 - Each of five varieties of corn are planted in...Ch. 12.2 - Prob. 5QCh. 12.2 - Prob. 6QCh. 12.2 - Prob. 7QCh. 12.2 - Prob. 8QCh. 12.2 - Prob. 9QCh. 12.2 - Verify the conclusion of Example 12.2.2 by doing a...
Ch. 12.2 - Prob. 12QCh. 12.2 - Prob. 13QCh. 12.3 - Prob. 1QCh. 12.3 - Prob. 2QCh. 12.3 - Intravenous infusion fluids produced by three...Ch. 12.3 - Construct 95%Tukey intervals for all ten pairwise...Ch. 12.3 - Prob. 5QCh. 12.3 - Prob. 6QCh. 12.3 - Prob. 7QCh. 12.4 - The cathode warm-up time (in seconds) was...Ch. 12.4 - Test the hypothesis that the average of the true...Ch. 12.4 - In Case Study 12.2.1 test the hypothesis that the...Ch. 12.4 - Prob. 4QCh. 12.4 - Prob. 5QCh. 12.4 - For many years sodium nitrite has been used as a...Ch. 12.5 - Prob. 1QCh. 12.5 - Prob. 2QCh. 12.5 - Three air-to-surface missile launchers are tested...
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