Suppose y„ is a random sample from a distribution for which we only know the firs two moments E(y) = m and Var(y) = m(1 -F mc). (i) Find the quasi-likelihood Q(y,m)for m given c. Obtain the ma,mum quasi-likelihood estimate of m. Hems using Pearson Statistic obtain an estimate of c. Find a method of moment estimate of .

(a) The probability function of discrete random variable y

This distribution, denoted by NB(m,), caned a negative binomial distribution with mean m and dispersion parameter c.

(b) Suppose a,, • • • , — tae(,,, ) Show how You would nod maximum likelihood estimates a m. and c. Do you get explicit solution for any of more.

(c) Suppose y„ is a random sample from a distribution for which we only know the firs two moments E(y) = m and Var(y) = m(1 -F mc). (i) Find the quasi-likelihood Q(y,m)for m given c. Obtain the ma,mum quasi-likelihood estimate of m. Hems using Pearson Statistic obtain an estimate of c. Find a method of moment estimate of .

(d) The extended quasi-likelihood is defined as Q+ = —.(2,/Var(V)) + Q(Y,m,) Obtain maximum extended quasi likelihood estimating equation (i.e., az = o and .4+ lac = 0). Do you obtain explicit solution for
5. Consider the data ® below. The me of 71- and are = 0.0TAS and = o.orzsrz xin : 0/5,2/6,0/7,0/7,0/8, 0/8, 0/8, 1/2, 2/8,1/10

(i) By using the score test is there any evidence of over dispersion in the data?

(ii) using …to , Where the parameter used GLM to represent over-dispersion in binomial data.

Last Completed Projects