During a one-year period, the number of accidents per day was distributed as given below:
No. of Accidents ---------Days
0------------------------209
1------------------------111
2-------------------------33
3--------------------------7
4--------------------------3
5--------------------------2
the maximum likelihood estimates are lambda^=0.6 for the Poisson distribution and r^=2.9 and beta^=0.21 for the Negative Binomial distribution. Conduct the likelihood ratio test for choosing between the two models.
My question is, when I go to solve for the likelihood I don't know how to obtain p(1), p(2),... for the Neg. Binomial? That is, how do I solve
(2.9Choose1), (3.9Choose2), etc... to solve for the logliklihood? (Especially on an exam where I only have my calculator?)
Thanks
No. of Accidents ---------Days
0------------------------209
1------------------------111
2-------------------------33
3--------------------------7
4--------------------------3
5--------------------------2
the maximum likelihood estimates are lambda^=0.6 for the Poisson distribution and r^=2.9 and beta^=0.21 for the Negative Binomial distribution. Conduct the likelihood ratio test for choosing between the two models.
My question is, when I go to solve for the likelihood I don't know how to obtain p(1), p(2),... for the Neg. Binomial? That is, how do I solve
(2.9Choose1), (3.9Choose2), etc... to solve for the logliklihood? (Especially on an exam where I only have my calculator?)
Thanks
Past SOA question
