ABSTRACT
In this section we are considering doubly censored samples from a normal distribution with pdf (2.2.1). The likelihood function as defined by (1.5.6) in this case becomes
The sample is censored on the left at T1 and on the right at T2 • There are c 1 censored observations less than T1, c2 greater than T2 , and n complete (uncensored) observations in the interaval T1 ::::; x ::::; T2 • The total sample size is N, where N = c1 + c2 + n. To obtain maximum likelihood estimators of J.t and a, we take logarithms of (3.3.1), differentiate with respect to these parameters, and equate to zero. The resulting estimating equations are
We define
D 1 = ~ <!>(~ 1 ) = ~ Q(- ~ 1 ), and n <1>(~ 1 ) n
(3.3.2)
(3.3.3)
where Q(~) is defined by (2.2.11) and the estimating equations of (3.3.2) may be reduced to
(x - !J-) = a(DJ - Dz), (3.3.4) s2 + (x-1-1)2 = a 2[1 + ~,D1 - ~202].
