# Accession Number:

## AD0469635

# Title:

## CORRELATION IN A BIVARIATE NORMAL DISTRIBUTION WHEN THE CONDITIONAL VARIANCES ARE KNOWN,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CA

# Personal Author(s):

# Report Date:

## 1965-08-01

# Pagination or Media Count:

## 27.0

# Abstract:

This paper considers the problems of estimation and hypothesis testing for the correlation coefficient in a non-singular bivariate normal distribution when the conditional variances are known. Such problems arise, for example, when each of the variables can be measured by an instrument, with the other variable held fixed, and the instrument manufacturers specify the precision of the instrument. It is shown that the statistic of interest in this problem is the sample covariance, v. The distribution of v is derived, in addition to its moments, some properties, and its asymptotic behavior. Some percentage points of the null distribution are tabulated. It is shown that the distribution has the monotone likelihood ratio property in the correlation coefficient parameter, rho. Uniformly most powerful level alpha tests of rho are given, and the distribution of the maximum likelihood estimator of rho is developed. Author