ABSTRACT
Since the transformed lognormal distribution is normally distributed, the asymptotic variances and covariances of fl and & given in Chapters 2, 3, and 4 for the various truncated and censored samples from the normal distribution are also applicable here. The variance of an estimate of the threshold parameter 'Y based on a right censored sample of total size N should approximately equal the variance of a corresponding estimate from a complete sample. This result was given by Cohen (1951) as
Example 6.1. In order to illustrate computational procedures involved in calculating parameter estimates from a single right censored sample from a lognormal population, an example originally given by Cohen (1951) and subsequently used by Cohen and Whitten (1988) has been selected. The complete sample consists of N = 20 randomly chosen observations from a lognormal distribution in which 'Y = 100, ~ = 50 (!J. = In~ = 3.912023), and CJ" = 0.4 (w = 1.3219144). Individual observations listed in order of magnitude are tabulated as follows:
A Random Sample from a Lognormal Population
127.211 135.880 153.070 166.475
128.709 137.338 155.369 168.554 131.375 144.328 155.680 174.800 132.971 145.788 157.238 184.101
133.143 148.290 164.304 201.415
For the purpose of this illustration, the sample is considered to be Type II censored with c = 2 at T = y 18,20 = 174.800. For the censored sample, N = 20, n = 18, c = 2, and h = c!N = 2/20 = 0.1. The only information assumed to be known about the two censored observations is that they exceed 174.800. We illustrate only the MMLE as this is usually the preferred estimator when samples are small.
