Karl Pearson in Russian Contexts |
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Authors: | Eugene Seneta |
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Institution: | School of Mathematics and Statistics, FO7, University of Sydney, NSW 2006, Australia E-mail: |
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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. |
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Keywords: | English Biometric School interpolation linear least squares orthogonal polynomial expansions Pearson's system of curves skewness Scandinavian Statistical School Karl Pearson Chebyshev Markov Chuprov Slutsky Bernstein Romanovsky Krawtchouk Isserlis Orzhentskii Lakhtin Mitropolskii |
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