M. G. Kendall

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Geometrical Probability

By M. G. Kendall

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Maurice Kendall

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Sir Maurice George Kendall (September 6, 1907-March 29, 1983) was a British statistician.


Maurice Kendall was born in Kettering, Northhamptonshire as the only child of John Roughton Kendall and Georgina Brewer. As a young child he survived a case of cerebral meningitis, which was at the time frequently fatal. After growing up in Derby, England, he studied mathematics at St. John's College, Cambridge, where he played cricket and chess (with future champions Conel Hugh O'Donel Alexander and Jacob Bronowski). After graduation as a Mathematics Wrangler in 1929, he joined the British Civil Service in the Ministry of Agriculture. In this position he became increasingly interested in using statistics towards agricultural questions, and one of his first published papers to the Royal Statistical Society involved studying crop productivity using factor analysis. He was elected a Fellow of the Society in 1934.

In 1938 and 1939 he began work, along with Bernard Babington Smith, on the question of random number generation, developing both one of the first early mechanical devices to produce random digits, and formulated a series of tests for statistical randomness in a given set of digits which, with some small modifications, became fairly widely used. He produced one of the second large collections of random digits (100,000 in total, over twice as many as those published by L. H. C. Tippett in 1927), which was a commonly used tract until the publication of RAND Corporation's A Million Random Digits with 100,000 Normal Deviates in 1955 (which was developed with a roulette wheel-like machine very similar to Kendall's and verified as "random" using his statistical tests).

Kendall and Babington Smith used four separate tests to determine whether a given sequence of digits was "random" (or "unordered"). The first was a frequency test, which looked to make sure that the count of each digit in a sequence was close enough to expected probabilities ("close enough" was determined by the use of a chi square calculation). If one were rolling an ideal six-sided die, over the long run one would expect to get an equal number of ones, twos, threes, etc. The second test was a serial test, which looked at the expected and observed frequencies of pairs of two digits (01, 11, 12, etc.), which got around the problem of sequences such as "1234512345" which would pass the frequency test but be decidedly non-random. The third test was another type of frequency test, this time for the expected and found set of five-digit sequences, known as a poker test, after the card game. The fourth test was known as the gap test, which looked for expected gaps between individual digits (usually between zeros) in long sequences, comparing observed counts ("01230" would be a gap of three digits between the zeros, "0120" would be two, etc.) with their statistical probabilities. If a set of numbers passed all four tests, it was considered by Kendall and Babington Smith to be "random enough" for most usage. They also developed the notion of "local randomness", noting that in any sufficiently long sequence of truly random digits there would be sets which would look exceedingly unrandom (such as a string of many zeros together). They concluded that these small cases of local un-randomness in an overall random sequence should not be discarded, but that care must be taken in the uses of random number sequences to make sure such "patches" of data did not overly add bias to the results.

In 1937, he additionally aided the aging statistician G. Udny Yule in the revision of his standard statistical textbook, Introduction to the Theory of Statistics, commonly known for many years as "Yule and Kendall". The two had met by chance in 1935, and were on close terms until Yule's death in 1951 (Yule was godfather to Kendall's second son).

During this period he also began work on the rank correlation coefficient which currently bears his name (Kendall's tau), which eventually led to a monograph on Rank Correlation in 1948.

In the late 1930s, he was additionally part of a group of five other statisticians who endeavored to produce a reference work summarizing recent developments in statistical theory, but it was cancelled on account of onset of World War II. Kendall became Assistant General Manager to the British Chamber of Shipping by day and had air-raid warden duties by night. Despite these constraints on his time, he managed to produce volume one of The Advanced Theory of Statistics in 1943 and a second volume in 1946.

During the war he also produced a series of papers extending to work of R.A. Fisher on the theory of k-statistics, and developed a number of extensions to this work through the 1950s. After the war, he worked on the theory and practice of time series analysis, and conclusively demonstrated (with the meager computing resources available at the time) that unsmoothed sample periodograms were unreliable estimators for the population spectrum.

In 1949 he accepted the second chair of statistics at the London School of Economics at the University of London, and worked part-time as the director of the new Research Techniques Division. From 1952 to 1957 he edited a two-volume work on Statistical Sources in the United Kingdom, which was a standard reference until the mid-1970s. In the fifities he also worked on multivariate analysis, and developed the text Multivariate Analysis in 1957. In the same year he also developed, along with W. R. Buckland, a Dictionary of Statistical Terms, aimed at helping making the tools of statistics more available to potential users in industry and government.

In 1953 he published " The Analytics of Economic Time Series, Part 1: Prices" in which he suggested that the movement of shares on the stock market was random i.e. they were as likely to go up on a certain day as they were to go down. These results were disturbing to some financial economists and further debate and research then followed. This ultimately led to the creation of "The Efficent Market Hypothesis" which states that random price movements indicate a well-functioning or efficient market.

In 1961 he left the University of London and took a position as the managing director (later chairman) of a consulting company, CEIR (later known as Scientific Control Systems), and in the same year began a two-year term as president of the Royal Statistical Society. In the 1960s he published and co-edited a number of volumes and monographs in statistical theory.

In 1972, he became director of the World Fertility Survey, a project sponsored by the International Statistical Institute and the United Nations which aimed to study fertility in developed and developing nations. He continued this work until 1980, when illness forced him to retire.

He was knighted by the British government in 1974 for his services to the theory of statistics, and received the Peace Medal of the United Nations in 1980 in recognition for his work on the World Fertility Survey. He was also elected a fellow of the British Academy and received the highest honor of the Royal Statistical Society, the Guy Medal in Gold. He additionally had served as president of the Operational Research Society, the Institute of Statisticians, and was elected a fellow of the American Statistical Association, the Institute of Mathematical Statistics, the Econometric Society, and the British Computer Society. At the time of his death in 1983, he was honorary president of the International Statistical Institute.


  • M.G. Kendall and B. Babington Smith, "Randomness and Random Sampling Numbers," Journal of the Royal Statistical Society 101:1 (1938), 147-166.
  • M.G. Kendall and B. Babington Smith, Tables of Random Sampling Numbers (Cambridge, England: Cambridge University Press, 1939).
  • Keith Ord, "In Memoriam: Maurice George Kendall, 1907-1983", The American Statistician 38:1 (Feb 1984), 36-37.
  • Alan Stuart, "Sir Maurice Kendall, 1907-1983", Journal of the Royal Statistical Society, Series A (General) 147:1 (1984), 120-122.
  • Alan Stuart and Keith Ord, Kendall's Advanced Theory of Statistics Volume 1 - Distribution Theory (Sixth Ed.), 1994

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