# Accession Number:

## AD0680438

# Title:

## GENERALIZATION OF RATIO ESTIMATE FOR POPULATION TOTAL,

# Descriptive Note:

# Corporate Author:

## SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1968-10-01

# Pagination or Media Count:

## 16.0

# Abstract:

It is desired to estimate the total Y for a finite population of size N with unknown values. A population with corresponding known values is available. Also, a simple random sample of size n is taken from the unknown population. Let y bar be the mean of the sample while x bar is the mean of the n values from the known population that correspond to these sample values. The ratio estimate of Y is generalized to the form NX bary barAx bar1-AX bar, where X bar is the mean of the known population. Use of A A sub o suitably chosen, yields an estimate that approximately is unbiased and has as small a variance as is attainable for a linear regression estimate. When A sub o is unknown in advance, it can be estimated denoted by A sub o. An estimate is developed for the standard deviation of the estimate using A sub o. Also, an estimate is obtained for the standard deviation of this estimate for the standard deviation. Finally, some comparisons are made with the linear regression estimate. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability