ABSTRACT
When they exist, maximum likelihood esimates e, X.~> X.2 , can be found by simultaneously solving the preceding system of equations. However, regardless of the form assumed by f(x; A.~> A.2), the estimate of e follows from the first equation of (14.3.10) as
N (14.3.11)
Estimates of the remaining parameters can be obtained as the simultaneous solution of a In L/ilA.j = 0, j = 1 ,2, which derives information only from the nonzero sample observations and is the same system of estimating equations obtained in Chapter 13 for a truncated distribution with missing zero class. The estimate of w follows from (14.3.7) as
- j(O). (14.3.12)
For the Poisson distribution, the alternate probability function (14.3.8) becomes
X= 1, 2, ... , (14.3.13)
Maximum likelihood estimating equations based on this probability function are
and the resulting estimators are , n 6=-N'
A. x* =---1 - e-"''
in agreement with those given in (14.3.6).
