Karl Pearson's Influence in the United States

Karl Pearson, the founder of mathematical statistics, was the leading statistical researcher from the 1890s up to about 1920. His interests were wide-ranging and so his impact on statistics in the United States was also wide-ranging. Many American researchers came to University College London to study with him. Others studied his work from afar. In the United States, Pearsonian statistics first penetrated the academic landscape in biology. This was soon followed by the fields of economics and psychology. It was not until relatively late in Pearson's career that several American mathematicians took up statistics as a serious research topic.     

Karl Pearson and the Establishment of Mathematical Statistics

At the end of the nineteenth century, the content and practice of statistics underwent a series of transitions that led to its emergence as a highly specialised mathematical discipline. These intellectual and later institutional changes were, in part, brought about by a mathematical-statistical translation of Charles Darwin's redefinition of the biological species as something that could be viewed in terms of populations. Karl Pearson and W.F.R. Weldon's mathematical reconceptualisation of Darwinian biological variation and "statistical" population of species in the 1890s provided the framework within which a major paradigmatic shift occurred in statistical techniques and theory. Weldon's work on the shore crab in Naples and Plymouth from 1892 to 1895 not only brought them into the forefront of ideas of speciation and provided the impetus to Pearson's earliest statistical innovations, but it also led to Pearson shifting his professional interests from having had an established career as a mathematical physicist to developing one as a biometrician. The innovative statistical work Pearson undertook with Weldon in 1892 and later with Francis Galton in 1894 enabled him to lay the foundations of modern mathematical statistics. While Pearson's diverse publications, his establishment of four laboratories and the creation of new academic departments underscore the plurality of his work, the main focus of his life-long career was in the establishment and promulgation of his statistical methodology.     

Karl Pearson and the Scandinavian School of Statistics

The relationship between Karl Pearson and the Scandinavian statisticians was more of a competitive than a collaborative nature. We describe the leading statisticians and stochasticists of the Scandinavian school, and relate some of their work to the work of Pearson.     

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

Karl Pearson's work greatly inspired P. C. Mahalanobis's interest in statistics, who was at the centre of modern statistical developments in India. Mahalanobis learned statistics on his own, reading Pearson's articles and his journal, and encouraged others to study Pearson's papers. Pearson was a Honorary Fellow of the Indian Statistical Institute, which has been a leading statistical training and research center in India. The statistical revolution that Pearson brought also facilitated the training and research of many Indian statisticians.     

Karl Pearson—The Scientific Life in a Statistical Age by Theodore M. Porter: A Review

Porter presents an excellent account of the young Karl Pearson and his extraordinarily varied activities. These ranged from the Cambridge Mathematical Tripos Exams to German history and folklore, and included free thought, socialism, the woman's question, and the law. Returning to science, Pearson produced the famous Grammar of Science . He decided on a career in statistics only at age 35. Porter emphasizes Pearson's often acrimonious but largely successful battles to show the wide applicability and importance of statistics in many areas of science and public affairs. Eugenics became a passion for Pearson. Avoiding all formulas Porter fails to give any concrete ideas of even Pearson's most important contributions to statistical theory. We try to sketch these here.     

Boekbespreking

Book reviewed in this article: Slippage tests, R. DOORNBOS Markov Processes and Potential Theory, Proceedings of an Advanced Symposium Conducted by the Mathematics Research Center, United States Army Varianzanalyse, HEINZ AHRENS Joint Statistical Papers of J. Neyman and E. S. Pearson A Selection of Early Statistical Papers of J. Neyman Statistical Methods in Engineering Experiments, E. M. BARTEE Ökonometrische Prognosen, G. MENGES Papers on National Income and Allied Topics, Vol. III, edited by N. S. R. SASTRY, V. M. DANDEKAR, S. G. TIWARI and UMA DATTA Die Messung des technischen Fortschritts im Rahmen des gesamtwirtschaftlichen Wachstums-prozesses, FLORIAN H. FLECK Surrey Sampling, LESLIE KISH Handbook of mathematical psychology, Vols. I, II and III, R. DUNCAN LUCE, ROBERT R. BUSH and EUGENE GALANTER Readings in mathematical psychology, Vols. I and II, R. DUNCAN LUCE, ROBERT R. BUSH and EUGENE GALANTER (Eds.)     

Karl Pearson and the Origin of Kurtosis

Although the kurtosis index proposed by Karl Pearson in 1905 is introduced in statistical textbooks at all levels, the measure is not easily interpreted and has been a subject of considerable debate. In this study, the theoretical development of kurtosis is surveyed from a historical perspective of Pearson's work on evolution. It surprisingly emerges that there was no emphasis in Pearson's papers on kurtosis as measuring (in part) tail heaviness. However, it is found that Pearson used to frequently adjust the formalisation of kurtosis depending on his changing needs. This complex development partly explains the confusion that would surround kurtosis in subsequent literature. Our conclusion is that most misunderstandings arise from improper use of the kurtosis coefficient outside the Pearson system of frequency curves.     

Statistical Regularity and Free Will: L.A.J. Quetelet and P.A. Nekrasov

In the 19th century, causes of empirically observed stability of averages in settings relating to human behaviour were a topic of intense discussion in western Europe. This followed an extensive study of empirical stability by the founder of modern statistics (and of the International Statistical Institute) L.A.J. Quetelet, published in 1835, in what he called "Social Physics". The eminent mathematician of strong probabilistic and philosophical inclination and Russian Orthodox religious belief, P.A. Nekrasov, took up and modified Quetelet's Social Physics in 1902, with (social) independence seen as prime cause of statistical regularity. Our paper focuses on the role free will plays in the statistical writings of Quetelet and of Nekrasov. The work of the latter has remained little known in general, mainly for politico-ideological reasons.     

Book reviews

A Restatement of Economic Liberalism Samuel Brittan Macmillan Japanese Style Management Transferred: The Experience of East Asia K. John Fukuda Routledge Japanese Management in America and Britain Donald Duncan Gordon Gower The Japanization of British Industry Nick Oliver Barry Wilkinson The Finances of British Trade Unions 1975–1985 Paul Willman Industrial Relations in Small Firms—Small Isn’t Beautiful Al Rainnie Routledge Managers of Discontent: Trade Union Officers and Industrial Relations Managers Diane Watson Routledge Recruitment and Selection in the Labour Market Paul Windolf and Stephen Wood Gower Safety at work: the limits of self-regulation Sandra Dawson, Paul Willman, Martin Bamford and Alan Clinton Debating Coal Closures: Economic Calculation in the Coal Dispute 1984–5 David Cooper and Trevor Hopper Helping the Unemployed Professional Roland Pearson and Anne Heyno Wiley Incompressible Unemployment John Naylor and Barbara Senior Avebury The Individual in the Economy: A Survey of Economic Psychology Stephen E. G. Lea, Roger M. Tarpy Financial and Economic Analysis of Enterprises Karl Hedderwick     

Boekbespreking

Book reviewed in this article:
Receptbladen voor de statistische verwerking van waarnemingen
Handbook of the Poisson Distribution, FRANK A. HAIOHT, John Wiley & Sons
Bibliography on time series and stochastic processes, H. O. A. WOLD (editor), Oliver & Boyd
L'car;estimation statistique, DANIEL DUMAS de RAULY, Gauthier-Villars
Time Series Analysis Papers, E. PARZEN
Statistics, L. H. C. TIPPETT
Statistische Tabellen, W. WETZEL, M. D. JÖHNK und P. NAEVE
Bayesian decision problems and Markov chains, J. J. MARTIN
Introduction to Probability and Statistical Decision Theory, G. HADLEY
Statistical Methods in Economics, H. W. GUTHRIE, Richard D. Irwin
Papers on regional statistical studies, (onder redactie van SYLVIA OSTRY en T. K. RYMES)
Intermediate economic statistics, KARL A. Fox, John Wiley and Sons
Introduction to mathematical sociology, J. S. COLEMAN     

Boekbespreking

Book reviewed in this article: Receptbladen voor de statistische verwerking van waarnemingen Handbook of the Poisson Distribution, FRANK A. HAIOHT, John Wiley & Sons Bibliography on time series and stochastic processes, H. O. A. WOLD (editor), Oliver & Boyd L'car;estimation statistique, DANIEL DUMAS de RAULY, Gauthier-Villars Time Series Analysis Papers, E. PARZEN Statistics, L. H. C. TIPPETT Statistische Tabellen, W. WETZEL, M. D. JÖHNK und P. NAEVE Bayesian decision problems and Markov chains, J. J. MARTIN Introduction to Probability and Statistical Decision Theory, G. HADLEY Statistical Methods in Economics, H. W. GUTHRIE, Richard D. Irwin Papers on regional statistical studies, (onder redactie van SYLVIA OSTRY en T. K. RYMES) Intermediate economic statistics, KARL A. Fox, John Wiley and Sons Introduction to mathematical sociology, J. S. COLEMAN     

Pearson's Statistics in the Netherlands and the Astronomer Kapteyn

In 1903 the well-known Dutch astronomer Kapteyn published a paper in which he discussed statistical methods which he thought would be relevant for biologists. His motivation was the 1895 paper of Pearson on skew frequency curves. Kapteyn had concluded that the theory was open to grave objections and was not adapted to nonmathematical readers. He was then led to an independent investigation of the subject. This publication would lead to a heated dialogue between Kapteyn and Pearson, in which they accused each other of inappropriate starting points, of plagiarism and of making serious mathematical mistakes. This article evaluates these claims. In addition, Kapteyn's struggle to make his work accessible to biologists is discussed.     

Tests based on φ-divergences for bivariate symmetry

In this paper we introduce a family of test statistics for testing symmetry based on φ-divergence families. These test statistics yield the likelihood ratio test and the Pearson test statistic as special cases. Asymptotic distribution for the new test statistics are derived under both the null and the alternative hypotheses. A simulation study is presented to see that some new test statistics offer an attractive alternative to the classical Pearson test statistic for the problem of symmetry. Received: May 2000     

On the Bicentenary in St. Petersburg of Jacob Bernoulli's Theorem

We focus on the Bicentenary (1913) celebrations, organised in St. Petersburg, Russia, by the great probabilist, A. A. Markov, founder of the theory of Markov chains. This theory was stimulated by the need to demonstrate a Law of Large Numbers for sums of dependent random variables. Markov's work on the Law of Large Numbers originating in the celebrations was exposited and extended by S. N. Bernstein and, in English, by J. V. Uspensky, who had played an integral part in the St. Petersburg celebrations. Copyright © 2014 John Wiley & Sons, Ltd.     

The Language of the English Biometric School

This paper considers the language devised by Karl Pearson and his associates for discussing distributions, populations and samples, the basic language for frequentist inference. The original language—some of which is still in use—is described and also the changes it underwent under the influence of R.A. Fisher and of Russian and American mathematicians. The period covered is roughly 1890–1950.     

Boekbesprekingen

Book reviewed in this article:
"Netwerkplanning volgens PERT", Oorspronkelijke uitgave Federal Electric Corporation. Voor Nederland bewerkt door H. POOLMAN Jr en TH. M. FEMER.
Group representations and applied probability, E. J. HANNAN
Wahrscheinlichkeit und Information, A. M. YAGLOM und J. M. YAGLOM
Linear programming and the theory of the Arm, K. E. BOULDING en W. A. SPIVEY
Einftihring in die matbematische Statistik, L. SCHMETTERER
Recent results in information theory, S. KOTZ
Formeln und Tabellen der mathematischen Statistik, U. GRAF, H. J. HENNINO en K. STANGE
The elements of probability theory and some of its applications, H. CRAMER
Quality control and industrial statistics, ACHESON J. DUNCAN
Méthodes Statistiques de ľéonometrie, E. MALINVAUD
Wahrscheinlichkeitstheorie, H. RICHTER
Linear statistical inference and its applications, C. R. RAO, Wiley
Gebouw en getal - capita aselecta uit het bouwen en de statistiek, aangeboden aan JAN VAN ETTINGER
The Mathematical Approach to Biology and Medicine, NORMAN T. J. BAILEY
Zum Problem der Produktionsplanung in Ein- und Mehrproduktunternehmen, W. DINKEL-BACH
[1] Die grundlagen der Theorie der Markoffschen Prozesse, E. B. DYNKYN
[1a] Theory of Markov processes, E. B. DYNKYN
[1b] Markov Processes, 2 delen, E. B. DYNKYN
[2] Probability and related topics in physical sciences, M. KAC, Interscience publ., London, 1959.
[3] Markov chains with stationary transition probabilities, K. L. CHUNG
[4] Probabilités et potentiel, P. A. MEYER
[4a] Probability and potentials, P. A. MEYER
[4b] Processus de Markov, P. A. MEYER
[5] Intégration, N. BOURBAKI
[6] Principles of random walk, F. SPITZER
[7] An introduction to probability theory and its applications, second edition, W. FELLER     

Applications of the Likelihood Theory in Finance: Modelling and Pricing

This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their meaning can be translated to the world of mathematical finance and vice versa. A lot of similarities can be expressed in terms of LeCam’s theory for statistical experiments which is the theory of the behaviour of likelihood processes. For positive prices the arbitrage free financial assets fit into statistical experiments. It is shown that they are given by filtered likelihood ratio processes. From the statistical point of view, martingale measures, completeness, and pricing formulas are revisited. The pricing formulas for various options are connected with the power functions of tests. For instance the Black–Scholes price of a European option is related to Neyman–Pearson tests and it has an interpretation as Bayes risk. Under contiguity the convergence of financial experiments and option prices are obtained. In particular, the approximation of Itô type price processes by discrete models and the convergence of associated option prices is studied. The result relies on the central limit theorem for statistical experiments, which is well known in statistics in connection with local asymptotic normal (LAN) families. As application certain continuous time option prices can be approximated by related discrete time pricing formulas.     

I.J. Bienaymé [1796–1878]: Criticality,Inequality, and Internationalization*

Two striking contributions of Bienaymé to mathematical statistics: (1) a completely correct statemet of the Criticality Theorem for simple branching processes in 1845; and (2) the derivation of the Bienaymé-Chebyshev Inequality, are revisited on the 200th anniversary of his birth. We use writings and archival materials available since the note of Heyde & Seneta (1972) to present a fuller biographical picture. Bienaymé's connections with Buniakovsky and Chebyshev are elucidated, and this role in furthering Chebyshev's international contacts outlined. A concluding section illuminates Bienaymé's understanding of the linear regression of one random variable on another in an actuarial context of random shocks.     

校企产学研战略联盟技术创新驱动力的形成模式

我国的技术创新不仅依赖于外部引进和自主创新,合作创新更是发挥着重要的作用。校企产学研战略联盟作为合作创新的一种全新的组织模式,能够有效的整合校企双方的资源,更好的实现技术创新的目的,校企双方合作进行技术创新的驱动力显然区别于一般形式的合作创新。本文在对校企产学研战略联盟面对的环境因素、校企进行技术创新的动力因素及两者之间的相互作用进行分析的基础上,对校企产学研战略联盟技术创新驱动力的形成模式进行探讨。