A Discrete Analogue of Terrell’s Characterization of Rectangular Distributions
Nickos
Papadatos
1 *
1
National and Kapodistrian University of Athens, Department of Mathematics, Section of Statistics and Operations Research, Panepistemiopolis, 15784
Athens, Greece
Correspondence to:
*e-mail: npapadat@math.uoa.gr, users.uoa.gr/ npapadat/
June 2, 2022
Abstract—Terrell [18] showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and the equality is attained only for rectangular (uniform over some interval) distributions. In the present note it is proved that the same is true for the discrete case, in the sense that the correlation coefficient attains its maximal value only for discrete rectangular (uniform over some finite lattice) distributions.
Keywords:
discrete rectangular distributionorder statisticsHahn polynomialsPearson coefficient of correlation
DOI: 10.3103/S1066530723020035