Understanding Karl Pearson's Influence on Italian Statistics in the Early 20th Century

Abstract

Karl Pearson's work strongly influenced the development of Italian statistics in the early 20th century. This paper reports some Italian contributions following Pearson's thought, which are probably less known outside Italy; for other Italian work, which was more successful internationally, just a brief description is given. Pearsonian topics are divided into three categories: curve systems, interpolation and correlation. For the first category, the contribution by F. De Helguero and F. Insolera is outlined. The former worked on dimorphic curves and developed a new family as a modification of the normal model; the latter dealt primarily with the problems arising when Pearson's curve system is applied to data that do not meet its basic assumptions. For interpolation, we recall a remarkable work by C. Gini, where Pearson's idea of minimizing geometrical distances of points from an interpolating line is discussed and extended. Contributions by G. Pietra and G. Bortolotti are discussed. Regarding correlation, where the Italian contribution was large, the paper focuses on the work by C.E. Bonferroni and G. Parenti, who extended Pearson's product-moment correlation "r" and Pearson's correlation ratio η to the general case of polynomial dependence. A discussion on the correct interpretation of η by Parenti is reported. Copyright (c) 2009 The Author. Journal compilation (c) 2009 International Statistical Institute.

Discussion

“…As Borroni () explains, the skew‐symmetric distributions of Family 1 can be traced to de Helguero () and arose, along with his interest in dimorphic distributions, out of his criticism of Pearson's family of distributions. His work on dimorphic distributions was published in Biometrika and appears to have received support from Pearson, but his paper on perturbed distributions appeared in the less well‐read Italian journal after de Helguero's death, at the age of 28 years, in the 1908 Messina earthquake.…”