Here's the question:
1- The Number of claims on an auto comprehensive policy follows a geometric distribution w/ mean 0.6. (Which I know is a Neg Binomial w/ (r=1, B=0.6))
2-The number of claims for each insured follows a poisson distribution w/ parameter lambda.
3- Lambda varies by insured according to a gamma distribution.
Calculate the proportion of insureds for which the expected number of claims per year is less than 1.
__________________________________________________ _______________
**When you do the calculations, Beta=Theta=0.6 and r=alpha=1**
My main issue is how to determine whether to use the neg binomial probability that n<1 or the gamma probability that n<1. I understand the solution uses F(1) for an exponential, which is a gamma. But, initially I was using the neg binomial probability that n<1 instead of the gamma. How do I determine which distribution to use? Thanks!
1- The Number of claims on an auto comprehensive policy follows a geometric distribution w/ mean 0.6. (Which I know is a Neg Binomial w/ (r=1, B=0.6))
2-The number of claims for each insured follows a poisson distribution w/ parameter lambda.
3- Lambda varies by insured according to a gamma distribution.
Calculate the proportion of insureds for which the expected number of claims per year is less than 1.
__________________________________________________ _______________
**When you do the calculations, Beta=Theta=0.6 and r=alpha=1**
My main issue is how to determine whether to use the neg binomial probability that n<1 or the gamma probability that n<1. I understand the solution uses F(1) for an exponential, which is a gamma. But, initially I was using the neg binomial probability that n<1 instead of the gamma. How do I determine which distribution to use? Thanks!
ASM 12.13