16. Annual claim numbers Xi are modeled by a Poisson distribution with unknown parameter A. Prior knowledge about A can be summarized by a uniform distribution on the interval [60, 120]. (a) Determine the form of the Bühlmann credibility estimator of the pure premium E(Xn+1) based on a random sample x of claim num- bers over n years. (b) What would the estimate be if X = (106, 105, 110, 98, 101, 113)?
16. Annual claim numbers Xi are modeled by a Poisson distribution with unknown parameter A. Prior knowledge about A can be summarized by a uniform distribution on the interval [60, 120]. (a) Determine the form of the Bühlmann credibility estimator of the pure premium E(Xn+1) based on a random sample x of claim num- bers over n years. (b) What would the estimate be if X = (106, 105, 110, 98, 101, 113)?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
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![16. Annual claim numbers Xi are modeled by a Poisson distribution with
unknown parameter A. Prior knowledge about A can be summarized by
a uniform distribution on the interval [60, 120].
(a) Determine the form of the Bühlmann credibility estimator of the
pure premium E(Xn+1) based on a random sample x of claim num-
bers over n years.
(b) What would the estimate be if X = (106, 105, 110, 98, 101, 113)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2F439f67f2-4460-4a1a-b53c-e63b5a0a75cb%2F5wsgpjd_processed.png&w=3840&q=75)
Transcribed Image Text:16. Annual claim numbers Xi are modeled by a Poisson distribution with
unknown parameter A. Prior knowledge about A can be summarized by
a uniform distribution on the interval [60, 120].
(a) Determine the form of the Bühlmann credibility estimator of the
pure premium E(Xn+1) based on a random sample x of claim num-
bers over n years.
(b) What would the estimate be if X = (106, 105, 110, 98, 101, 113)?
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