**UsageCounts**

{"references": ["A. M. Mathai, The concept of correlation and misinterpretations. International\nJournal of Mathematical and Statistical Sciences, 1998, 7: 157-167.", "R. A. Fisher, Distribution of the values of the correlation coefficient in\nsamples from an indefinitely large population. Biometrika, 1915, 10: 507-\n521.", "A. Winterbottom, A note on the derivation of Fisher-s transformation of\nthe correlation coefficient. The American Statistician, 1979, 33: 142-143.", "H. Hotelling, New light on the correlation coefficient and its transforms.\nJournal of Royal Statistical Society, Ser. B., 1953, 15: 193-232.", "A. K. Gayen, The frequency distribution of the product-moment correlation\ncoefficient in random samples of any size drawn from non-normal\nuniverses. Biometrika, 1951, 38: 219-247.", "D. L. Hawkins, Using U statistics to derive the asymptotic distribution\nof Fisher-s Z statistic. The American Statistician, 1989, 43: 235-237.", "S. Konishi, An approximation to the distribution of the sample correlation\ncoefficient. Biometrika, 1978, 65: 654-656.", "H.-T. Ha and S. B. Provost, A viable alternative to resorting to statistical\ntables. Communications in Statistics-Simulation and Computation, 2007,\n36: 1135-1151."]}

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.