You are given the following information about a book of business comprised of 100 insureds: N, (i) X, =E Y, is a random variable representing the annual loss of the f insured. J=1 N,, N2, ., N100 are independent random variables distributed according to a negative binomial distribution with parameters r (unknown) and ß = 0.2. (ii) (ii) Unknown parameter r has an exponential distribution with mean 2. Yn, Y2, .., YN, are independent random variables distributed according to a Pareto distribution with a = 3.0 and 0 = 1000. (iv) %3D Determine the Bühlmann credibility factor 7 for the book of business

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You are given the following information about a book of business comprised of 100 insureds:
N,
(i)
X, = Y, is a random variable representing the annual loss of the 1™ insured.
J-1
N, N2, .., N100 are independent random variables distributed according to a negative
binomial distribution with parameters r (unknown) and ß= 0.2.
(ii)
(ii)
Unknown parameter r has an exponential distribution with mean 2.
(iv)
Y1, Y2, ..., YIN, are independent random variables distributed according to a Pareto
distribution with a = 3.0 and 0 = 1000.
Determine the Bühlmann credibility factor, Z, for the book of business.
Transcribed Image Text:You are given the following information about a book of business comprised of 100 insureds: N, (i) X, = Y, is a random variable representing the annual loss of the 1™ insured. J-1 N, N2, .., N100 are independent random variables distributed according to a negative binomial distribution with parameters r (unknown) and ß= 0.2. (ii) (ii) Unknown parameter r has an exponential distribution with mean 2. (iv) Y1, Y2, ..., YIN, are independent random variables distributed according to a Pareto distribution with a = 3.0 and 0 = 1000. Determine the Bühlmann credibility factor, Z, for the book of business.
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