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In samples of this type, observation is possible only in the two tails of the distribution. Observation is not possible for T 1 < x < T2 • The sample consists of N = n = n1 + n 2 observations, where n1 observations are less than or equal to T1 and n2 observations arc greater than or equal to T2 • These samples differ from the centrally censored samples only in that in the truncated case, the value of cis unknown. The likelihood function of a sample of this type from a normal distribution is
We take logarithms of this equation, differentiate and equate to zero to obtain estimating equations
In order to simplify the notation and thereby reduce the estimating equations to forms that are analogous to corresponding equations for other types of doubly restricted samples, we define
1z(£1,£2) = <l>1 + (1 - <l>zf It is to be noted that V1 = (c!n)11 and V2 = (c!n)12 where V1 and V2 were
defined by (3 .4.3) in connection with estimators based on doubly censored samples for which the total number of censored observations was known but not the number in each tail separately.