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Frequency (number) of individual claims in each period, XE {0, 1, 2}, follow the binomial distribution (2, 0) and 0 follow distribution U(0, 1). Prediction of the frequency of claims in future periods using the Buhlmann. method c- ZR+ (- Z)H, Z = credibility factor, R = current observation, and H= prior mean process. a) Calculate E(0), E(0) and Var(0) b) Specify E(X0) and Var(X|0) c) Calculate the expected process variance E. Var. (x)) and the conditional mean variance Var (E. (X))) d) Calculate the ratio of the expected process variance to the E. (Var (X 8)) conditional mean variance, *= Vary (E (X 8))

Frequency (number) of individual claims in each period, XE {0, 1, 2}, follow the binomial distribution (2, 0) and 0 follow distribution U(0, 1). Prediction of the frequency of claims in future periods using the Buhlmann. method c- ZR+ (- Z)H, Z = credibility factor, R = current observation, and H= prior mean process. a) Calculate E(0), E(0) and Var(0) b) Specify E(X0) and Var(X|0) c) Calculate the expected process variance E. Var. (x)) and the conditional mean variance Var (E. (X))) d) Calculate the ratio of the expected process variance to the E. (Var (X 8)) conditional mean variance, *= Vary (E (X 8))

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Buhlmann's method
Frequency (number) of individual claims in each period, X € {0, 1, 2}, follow the binomial distribution (2, 0) and 0 follow distribution U(0, 1). Prediction of the frequency of claims in future periods using the Buhlmann. method c- ZR+ (- Z)H, Z = credibility factor, R = current observation, and H= prior mean process. a) Calculate E(0), E(0) and Var(0) b) Specify E(XO) and Var(X|0) c) Calculate the expected process variance E. Car, (x)) and the conditional mean variance Var; (E. (X))) d) Calculate the ratio of the expected process variance to the E. (Var (X 8)) conditional mean variance, k- Var, (E. (X 8)) e) Calculate the predicted number of claims in the second period if there are three claims in the first period, E(X₂X₁= 3).
Transcribed Image Text:Frequency (number) of individual claims in each period, X € {0, 1, 2}, follow the binomial distribution (2, 0) and 0 follow distribution U(0, 1). Prediction of the frequency of claims in future periods using the Buhlmann. method c- ZR+ (- Z)H, Z = credibility factor, R = current observation, and H= prior mean process. a) Calculate E(0), E(0) and Var(0) b) Specify E(XO) and Var(X|0) c) Calculate the expected process variance E. Car, (x)) and the conditional mean variance Var; (E. (X))) d) Calculate the ratio of the expected process variance to the E. (Var (X 8)) conditional mean variance, k- Var, (E. (X 8)) e) Calculate the predicted number of claims in the second period if there are three claims in the first period, E(X₂X₁= 3).
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