ABSTRACT
The presentation in this chapter is based on previous results of Cohen ( 1941, 1951). A method of higher moments is introduced and employed in the estimation of Pearson distribution parameters from truncated samples with known points of truncation. In the four-parameter distributions, the first six moments of a doubly truncated sample are required, but only the first five moments are needed from a singly truncated sample. The order of the highest-order moment involved in these estimators is equal to the number of distribution parameters plus the number of tails truncated. As a consequence of employing higher-order moments, sampling errors of estimates are somewhat greater than corresponding errors of maximum likelihood estimates. However, higher-moment estimates are consistent and they are functionly explicit. Nothing more complex than the inversion of a 5 x 5 matrix is involved in their calculation. Accordingly, they are suitable for use in large samples. Even in moderate-sized or small samples, they might be employed to provide first approximations to be used in iterating to maximum likelihood estimates.
