On some inequalities related to the range of some statistical indices (Q1901309)

This paper is a translation of an article by Carlo Benedetti which appeared in ibid. 18, No. 3/4, 102-125 (1957; Zbl 0089.361), where some bounds for the correlation coefficient in presence of isotonic correlation are derived. The original and interesting results presented in this work were also proved later through geometrical arguments by \textit{N. Georgescu-Roegen} [ibid. 19, No. 3/4, 38-45 (1959; Zbl 0099.356)]. Due to the interest shown in the literature for the problem dealt with in this work, we think that the reader may find this translation useful. A recent signal of this interest is a paper by \textit{T.-Y. Hwang} and \textit{C.-Y. Hu} [Stat. Probab. Lett. 19, No. 3, 195-198 (1994; Zbl 0791.62062)], where Benedetti's results have been rediscovered and proved again.