ESTIMATION OF POPULATION TOTALS FOR HIGHLY SKEWED
POPULATIONS IN REPEATED SURVEYS
Harold F. Huddleston
Statistical Reporting Service
U.S. Department of Agriculture
March 1965
ESTIMATION OF POPULATION TOTALS FOR HIGHLY SKEWED
POPULATIONS
IN REPEATED SURVEYS 1/
Introduction
The purpose of this report is to describe the investigation
of alter-
native estimators for extremely skewed distributions
based on prior knowledge
of the distributions.
The data considered in detail is the basic population
of area segments within a State.
However, the methods may be applied to any
type of sampling unit.
It is believed that the distributions
associated
with the segments for a particular State or group of States are similar for
the same characteristic
since standard rules of segment construction
were
used.
Procedures for combining the information
for the samples over years
in order to improve results are developed.
The alternative estimators require considerably more knowledge of the
distributions
than the mean and variance which are sufficient information for
determining sample size.
In fact, the basic objective is to make use of the
additional information which is available on the distribution
from the same
or similar populations.
While certain additional information
is required
about the nature of the distribution,
apriori knowledge about individual
sampling units is not required.
In the past, these estimators have been used
primarily to develop improved State or small area estimates.
These estimators may have small biases for individual States but the
biases can be made to sum to zero over a group of States.
A similar approach
for making estimates by districts or subdivisions within States has been
attempted on a limited basis.
One of the primary sources of variation in the estimators is the contri-
bution to the variance resulting from observations
in the right-hand tail of
positively skewed populations.
All the estimators studied are similar in
!! W. E. Kibler and Charles E. Caudill of the Research Branch assisted in
compil