Karl Pearson in Russian Contexts

Abstract

The confluence of statistics and probability into mathematical statistics in the Russian Empire through the interaction, 1910-1917, of A.A. Chuprov and A.A. Markov was influenced by the writings of the English Biometric School, especially those of Karl Pearson. The appearance of the Russian-language exposition of Pearsonian ideas by E. E. Slutsky in 1912 was instrumental in this confluence. Slutsky's predecessors in such writings (Lakhtin, Orzhentskii, and Leontovich) were variously of mathematical, political economy, and biological backgrounds. Work emanating from the interpolational nature of Pearson's system of frequency curves was continued subsequently through the work of Markov, Bernstein, Romanovsky, and Kravchuk (Krawtchouk), who laid a solid probabilistic foundation. The correlational nature in the interpolational early work of Chebyshev, and work of the English Biometric School in the guise of linear least-squares fitting exposited as the main component of Slutsky's book, was developed in population as well as sample context by Chuprov. He also championed the expectation operation in providing exact relations between sample and population moments, in direct interaction with Karl Pearson. Romanovsky emerges as the most adaptive and modern mathematical statistician. Copyright (c) 2009 The Author. Journal compilation (c) 2009 International Statistical Institute.

Karl Pearson and the Scandinavian School of Statistics

“…She came to London in 1915 to work at the Biometric laboratory, where she produced a paper on minimum chi‐squared estimation of the correlation coefficient (Smith, 1916). The same estimation idea had been put forward by Engledow & Yule (1914) for a different parameter, namely the recombination fraction in genetics, and by Slutsky (1913) for regression coefficients (Slutsky's paper had been rejected by Pearson; see section 5 of Seneta (2009) in this issue). Fisher did not like Smith's paper, and tried to publish a rejoinder, pointing out that the procedure would depend on the grouping used, but Pearson refused to accept it.…”

“…Gram developed the Gram–Schmidt orthogonalization (although discovered by Chebyshev, see Seneta, 2009 in this issue) and applied it to the derivatives of the normal density, leading to the series expansion, now named after him and the Swedish astronomer/statistician C. V. L. Charlier (although developed by Laplace, Poisson, and Bienaymé; cf. Hald, 2002).…”

Discussion

“…The historical background that follows identifies by whom and when they were proposed and why the fate of Families 2 and 3A was sealed, at least in the short term, by the hostile response they received from Karl Pearson. That hostility is well documented in the special edition of International Statistical Review published in 2009 in honour of Pearson and appears to have manifested itself in response to the criticism his famous “system of curves”, in modern‐day parlance, “family of distributions”, had received from the likes of de Helguero, Edgeworth, Kapteyn and Markov, the latter's criticism being especially vitriolic (Seneta, ). The main objection to his family was that Pearson provided no generating mechanisms for it.…”

Impact of Karl Pearson's Work on Statistical Developments in India

“…Incidentally, Pearson (1924) was stimulated by Romanovsky's (1923) recurrence formula for the central moments of the binomial ( n , p ) distribution. The statistical papers of Romanovsky and Pearson have a noticeable intersection; see the article by Seneta (2009) in this issue of the International Statistical Review . Both of them worked on coefficient of racial likeness, recurrence relations for moments and distribution curves.…”