ABSTRACT
When the results from (7 .2. 9) are substituted into (7 .2.6), the estimating equations become
where
a-y 13 i=l
tJVP.i=l I II
ap i=l
1 I - G(s;)
(7.2.10)
Solution of th~ three equations of (7 .2.10) for the three maximum likelihood estimates ('Y, 13, p) can be carried out by following the same procedure as that outlined for the solution of the inverse Gaussian estimating equations (7 .1.16). Evaluation of the third equation of (7 .2.1 0) involves complications that are similar to those involved in evaluation of the third equation of (7 .1.16). Here, for the gamma distribution, with p and thus cx3 , fixed, we solve the first two equations of (7 .2.10) for conditional estimates of 'Y and 13 and substitute directly into the loglikelihood equation (7.2.5) until we find the value of p or (cx 3 = 2/Vp) that maximizes this function, just as we did in calculating maximum likelihood estimates of IG parameters.
