Maurice George Kendall

Sir Maurice George Kendall , FBA (born September 6, 1907 in Kettering , Northamptonshire , † March 29, 1983 in Redhill , Surrey ) was a British statistician. The Kendall rank correlation coefficient and the Kendall concordance coefficient are named after him.

childhood and education

Maurice Kendall was in Kettering ( Northamptonshire born), the only child of John Roughton Kendall and Georgina Brewer. As a small child, he survived meningitis , which at the time was often fatal. He grew up in Derby ( England ) and studied mathematics at St. John's College ( Cambridge ). He also learned cricket and chess there and played with the later champions Conel Hugh O'Donel Alexander and Jacob Bronowski . After graduating from the University of Cambridge with a degree in mathematics , he took up a position in the British Civil Service of the Department of Agriculture in 1929 . Here he was increasingly interested in using statistics to solve agricultural questions. One of his first published work (at the Royal Statistical Society ) dealt with the analysis of grain yields using factor analysis . In 1934 he was elected a Fellow of the Royal Statistical Society.

Contributions to statistics

From 1938 he began to work together with the psychologist Bernard Babington-Smith († 1993) on questions of generating random numbers . In doing so, they developed one of the first early mechanical devices for generating random numbers, and developed a series of tests for randomness in a given set of digits that were widely used. They created one of the two great works with sequences of random sequences of digits. It contained 100,000 random digits, more than twice as many as the work by Leonard Henry Caleb Tippett (1902-1985) published in 1927 . Until the publication of A Million Random Digits with 100,000 Normal Deviates by RAND Corporation in 1955, the tables by Kendall and Babington were one of the most widely used. Roulette- like machines were used by both RAND Corporation and Kendall and Babington-Smith to generate the random number sequences . RAND Corporation used Kendall and Babington-Smith's tests to check the randomness of their digit sequences.

Kendall and Babington-Smith used four separate tests to determine whether a given sequence of numbers at random or disordered was:

1. The frequency test to check that the ten digits follow an even distribution .
2. The serial test , this time to check pairs of two digits for even distribution (01, 11, 12 etc.). For example, the sequence of digits 1234512345 would pass the frequency test but not the serial test.
3. The poker test , which checks the frequency of sequences of five digits (also for even distribution).
4. The gap test , which checks the lengths between two identical digits ( 01230 would be a three digit gap between zeros, 0120 would be a two digit gap, and so on). Theoretically, the length of the gaps follows a Poisson distribution .

They considered sequences of numbers that passed all four tests to be sufficiently random.

In modern statistics, all four tests are chi-square goodness-of-fit tests : the frequency test, the serial test, and the poker test are tests for a discrete equal distribution, and the gap test is a test for a Poisson distribution.

They also developed the concept of local randomness and found that in any sufficiently long sequence of true random numbers there are sequences that do not look random (e.g. a sequence of many zeros in a row). They concluded that these small cases of local randomness in sequences of random digits should not be discarded. However, when using such sequences, care must be taken not to distort the results too much.

In 1937 he assisted George Udny Yule in the revision of his widely used statistical textbook Introduction to the Theory of Statistics . The two had met by chance in 1935 and were close friends until Yule's death in 1951 (Yule was the godfather of Kendall's second son).

During this time he also began work on the rank correlation coefficient that bears his name: Kendall's Tau . This led to his monograph Rank Correlation in 1948. In the late 1930s he was also a member of a group with five other statisticians (including Egon Pearson and John Wishart ) who wanted to write a reference work for the latest developments in statistical theory. The Second World War prevented this, however.

In 1940, Kendall became an assistant general manager at the British Chamber of Shipping . Although he also took on night duties in air defense, he published the first volume of The Advanced Theory of Statistics in 1943 and the second volume in 1946. In parallel, he wrote a series of articles until 1950 that expanded the work of Ronald Aylmer Fisher on k-statistics. After the war he occupied himself with the theory and application of time series analysis ; Among other things, he showed that unsmoothed peridograms, calculated from sample data, are bad estimates.

London School of Economics

In 1949 Kendall received the second chair in statistics at the London School of Economics ( University of London ) and worked as the director of the new Research Techniques Division . From 1952 to 1957 he worked on his two-volume work The Sources and Nature of the Statistics of the United Kingdom , which was a standard work until the mid-1970s. In the 1950s, Kendall turned increasingly to multivariate statistics and published his work A course in multivariate analysis in 1957 . In the same year he published The Dictionary of Statistical Terms with William R. Buckland , which was intended to bring statistics to users in industry and government.

As early as 1953 he published the article The Analytics of Economic Time Series, Part 1: Prices , in which he hypothesized that changes in stock market prices can be viewed as random and that it is just as likely on a certain day that the stock price will rise or falls. The subsequent discussion and research led to the random walk theory and is closely related to the market efficiency hypothesis .

CEIR and World Fertility Survey

In 1961, Kendall left the University of London and became managing director (later also chairman) of the consulting firm CEIR, later known as Scientific Control Systems . That same year began his two-year presidency of the Royal Statistical Society. He published a number of other books in the 1960s, alone and with co-authors.

From 1972 Kendall was director of the World Fertility Survey , a project supported by the International Statistical Institute and the United Nations . The aim of the project was to record and study fertility in industrialized and developing countries. In 1980 he had to retire due to illness.

Honors

The Royal Statistical Society awarded Kendall the Guy Medal in silver in 1945 and in gold in 1968. In 1974 he was beaten for his services to statistics to the Knight Bachelor . In 1980 he received the United Nations Medal of Peace for his contributions to the World Fertility Survey.

He was a (elected) member of the British Academy , the American Statistical Association , the Institute of Mathematical Statistics , the Econometric Society , the British Computer Society and the Royal Statistical Society , among others . He was temporarily president of the Operational Research Society and the Institute of Statisticians . At the time of his death in 1983 he was Honorary President of the International Statistical Institute .

literature

• Keith Ord: In Memoriam: Maurice George Kendall, 1907-1983 . In: The American Statistician . 38, No. 1, 1984, pp. 36-37. JSTOR 2683557 .
• Alan Stuart: Sir Maurice Kendall, 1907-1983 . In: Journal of the Royal Statistical Society. Series A (General) . 147, No. 1, 1984, pp. 120-122. JSTOR 2981762 .
• DJ Bartholomew: Obituary: Sir Maurice Kendall FBA . In: Journal of the Royal Statistical Society. Series D (The Statistician) . 32, No. 4, 1983, pp. 445-446. JSTOR 2987557 .

Individual evidence

1. ^ John J. O'Connor, Edmund F. Robertson: Maurice George Kendall. In: MacTutor. October 2003, accessed October 12, 2011 . 
2. ^ Maurice George Kendall, Bernard Babington-Smith: Randomness and Random Sampling Numbers . In: Journal of the Royal Statistical Society . tape 101 , no. 1 . Blackwell Publishing, 1938, Sp. 147-166 , doi : 10.2307 / 2980655 .
3. ↑ Maurice George Kendall, Bernard Babington-Smith: Tables of Random Sampling Numbers . Cambridge University Press, Cambridge, England 1939.
4. ^ Leonard Henry Caleb Tippett: Random sampling numbers . Cambridge University Press, 1927.
5. ↑ Rand Corporation (Ed.): A Million Random Digits with 100,000 Normal Deviates . 1955, ISBN 978-0-02-925790-6 .
6. ↑ George Udny Yule, Maurice George Kendal: An introduction to the theory of statistics . 11th edition. C. Griffin, London 1937.
7. ↑ Maurice George Kendall: The Sources and Nature of the Statistics of the United Kingdom . Royal Society, London 1957.
8. ^ Maurice George Kendall: A course in multivariate analysis . Hafner Pub. Co, 1957.
9. ↑ Maurice George Kendall, William R. Buckland: The Dictionary of Statistical Terms . Oliver & Boyd Publishers and International Statistical Institute , 1957.
10. ^ Maurice George Kendall: The Analysis of Economic Time-Series-Part I: Prices . In: Journal of the Royal Statistical Society. Series A (General) . tape 116 , no. 1 . Blackwell Publishing, 1953, pp. 11-34 , doi : 10.2307 / 2980947 .