John N. Haddad and Serge B. Provost
Approximations to the Distribution of the Sample Correlation Coefficient
658 - 663
2011
5
4
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/13820
https://publications.waset.org/vol/52
World Academy of Science, Engineering and Technology
Given a bivariate normal sample of correlated variables,
(Xi, Yi), i 1, . . . , n, an alternative estimator of Pearson’s correlation
coefficient is obtained in terms of the ranges, Xi − Yi.
An approximate confidence interval for ρX,Y is then derived, and
a simulation study reveals that the resulting coverage probabilities
are in close agreement with the set confidence levels. As well, a
new approximant is provided for the density function of R, the
sample correlation coefficient. A mixture involving the proposed
approximate density of R, denoted by hR(r), and a density function
determined from a known approximation due to R. A. Fisher is shown
to accurately approximate the distribution of R. Finally, nearly exact
density approximants are obtained on adjusting hR(r) by a 7th degree
polynomial.
Open Science Index 52, 2011