Probability and Statistics on the Earliest Uses Pages

This is an INDEX to the PROBABILITY and STATISTICS entries on Jeff Miller’s Earliest Uses pages

Earliest Known Uses of Some of the Words of Mathematics

Earliest Uses of Various Mathematical Symbols .

These pages cover all branches of mathematics. The Words page is organised alphabetically with separate (large) files for each letter (printing out C would take 50 pages, but it’s exceptionally big!) and the Symbols page is organised by subject. The Symbols page has a section Symbols in Probability & Statistics.

The list here does not give every term described on the pages. It gives roots—e.g. the entry for alias covers one term and takes less than 30 words, while that for normal covers approximately 10 terms and takes over 700 words plus another 1000 on the Symbols page. Sy indicates there is material on Symbols in Probability & Statistics. The Symbols page has sections on combinatorial analysis, the normal distribution, probability and statistics.

Apart from a few terms from elementary combinatorics, the general mathematical terms used by statisticians/probabilists are not included in this index. Most can be found in the indexes for calculus and analysis, matrices and linear algebra and set theory and logic. For a general perspective on word-formation in mathematics see my Mathematical Words: Origins and Sources.

A – B A Abbe-Helmert criterion Admissibility Alias Alternative hypothesis Ancillary Analysis of Variance (see variance) Arithmetic mean Association Asymptotic Autocorrelation Autoregression Average B Bar chart Bar graph Bartlett adjustment or correction Bayes Behrens-Fisher Bell-shaped & bell curve Bernoulli distribution Bernoulli trial Bertrand’s paradox Beta distribution Bias Bimodal Binomial distribution Biometry Biostatistics Bivariate Black-Scholes formula Block & randomized block Bonferroni inequalities Boole’s inequality Bootstrap Borel-Cantelli lemmas Box-Cox transformation Box-Jenkins Branching process Brownian motion	C C Canonical correlation Cauchy distribution Censoring & Truncation Central limit theorem Central tendency (measures of) Cepstrum Chance & Doctrine of Chances Chaos Chapman-Kolmogorov equations Characteristic function Chebyshev polynomials Chebyshev’s inequality Chernoff bound Chi-square Classical probability Classical statistical inference Cluster analysis Cluster sampling Cochran’s thoerem Coefficient of variation Coherence Collective Combination Combinatorics Computer intensive Concomitant variable Conditional probability Sy Confidence interval Confounding Conjugate prior Consistency Contingency table Control chart Convolution Cornish-Fisher expansion Correlation Sy Correlogram Correspondence analysis Covariance Covariate Cramér-Rao inequality Cramér-von Mises test Criteria of estimation Criterion of sufficiency Critical region Critical value Cross-validation Cumulant Sy Curve fitting	D – E D Daniell window Data analysis Data mining Decile Decision theory Degrees of freedom Sy Dependent variable Descriptive statistics Design matrix Design of Experiments Deviance Dirichlet distribution Discriminant analysis Dispersion Distributed lag Distribution function Sy Dominance Dummy variable Durbin-Watson Dutch book E Econometrics Edgeworth expansion Effects (row, column, etc.) Efficiency Ehrenfest model EM algorithm Endogenous & exogenous Entropy Equiprobable Ergodic Error Errors in variables Estimation Event Sy Exchangeable Exhaustive estimation Expectation Sy Experiment Exponential Exploratory data analysis Extreme value
F – H F F distribution Sy Factor & factorial design Factor analysis Factorial Sy Fast Fourier transform Fiducial Filter Finite sample correction Fisher’s exact test Fisher information Fisher’s z transformation Fokker-Planck equation Frame (Sampling frame) Frequency distribution Frequency domain (see time domain) Frequentist G Gambler’s ruin Gamma distribution Gaussian Gauss-Markov theorem Generalized linear model GLIM Geometric distribution Geometric mean Goodness of fit Graduation H Harmonic analysis Harmonic mean Hat matrix Hazard rate Helmert transformation Hermite polynomial Heteroscedasticity Histogram Hypergeometric distribution Hypothesis testing	I – L I Identifiability Independence Index number Indicator Influence curve Information Information theory Interpolation Inter-quartile range Instrumental variables Inverse gaussian distribution Inverse probability Inverted gamma distribution J J-shaped Jacknife Jeffreys prior Jensen’s inequality  K k-statistics Sy Kalman filter Kaplan-Meier estimator Kernel Kolmogorov extension theorem Kolmogorov equation Kolmogorov-Smirnov Kriging Kullback-Leibler information Kurtosis L Lag Lagrange multiplier test Latin square Law of large numbers Law of iterated logarithm Law of small numbers Least squares (see Method of) Leptokurtic Leverage Life table Likelihood Likelihood ratio test Sy Lindley’s Paradox Link function Local probability Location and scale Logistic Logit Lognormal Lorenz curve Loss function	M - N M M-estimator Mahalanobis distance Markov chain Markov Chain Monte Carlo Markov process Markov’s inequality Martingale Mathematical expectation Mathematical statistics Maximum likelihood Maxwell distribution Mean Sy Mean error Mean square deviation Median Meta-analysis Method of least squares Sy Minimax Minimum χ^2 Mode Modulus Monte Carlo Monty Hall problem Moral expectation Morally certain Moving average Multicollinearity Multinomial distribution Multivariate Multivariate analysis N N-variate Negative binomial Neyman allocation Neyman-Pearson lemma Non-informative prior Non-normal Nonparametric Normal distribution Sy Normal equation Normal number Nuisance parameter Null hypothesis Sy
O – P O Odds Odds ratio Ogive Operating characteristic Operations Research Orthogonality Outlier  P p* formula P-value Parameter Pareto distribution Pascal’s triangle Pascal’s wager Path analysis Pearson curves Percentile Periodogram Permutation Permutation test Peters’ formula Pie chart Pivotal Poisson distribution Pólya and Pólya-Eggenberger Population Posterior & prior Power Sy Pre-whitening Principal components Principle of indifference (or principle of insufficient reason) Probability Sy Probability density function Sy Probability distribution Sy Probability distributions, names Probability integral transformation Probable error Probit Problem of the Nile Proportional hazard model Psychometrics	Q – R Q Quality control Quantile Quartile Quintile Queuing R Random number Random sample Random walk Random variable Sy Randomization Randomization test Randomized response Range Rank correlation Rao-Blackwell Rayleigh distribution Rectangular distribution Regression Sy Renewal theory Replication Residual Risk function Robustness Rule of succession	S S St Petersburg Paradox Sample Sample path Sample space Sampling distribution Scatter diagram Score Semi-invariant Sequential analysis Serial correlation Set Sheppard’s corrections Shrinkage Sign test Significance Similar region Simpson’s paradox Simulation Simultaneous equations model Size Sy Skew distribution Small sample problem Smoothing Spectrum Spline Spurious correlation Stable law Standard deviation Sy Standard error Standard score Standard normal curve Stanine Stationary stochastic process Statistic(s) Sy Statistical tables Stem-and-leaf display Stigler’s law of eponymy Stirling’s formula Stochastic Stratified sampling Strong law of large numbers Student's t distribution Sy Studentization Sufficiency Survival function
T T Tail Theory of games Theory of probability Time series Time domain Tramcar problem Treatment Trend Trimming Trivariate Truncation Type I error	U – V U U-statistic Unbiased Uniform distribution Uniformly most powerful Unimodal Univariate Utility V Variance Sy Variate Variate difference method Venn diagram Vital statistics Von Mises distribution	W – Z W Wald test Weibull distribution Weight & weighted White noise Wiener-Hopf Wiener process Wilcoxon tests Window Winsorized Wishart distribution Wold decomposition Y Yates's correction Youden square Yule or Yule-Simpson paradox Yule process Yule-Walker equations Z z-statistic Sy Zero-sum game

Other sources of information

The other main source for earliest uses information is H. A. David’s series of articles, “First (?) Occurrence of Common Terms in Mathematical Statistics.” There is substantial overlap between David’s list and the Earliest Uses list, though both lists reflect the interests of the contributors: David’s list has better coverage of experimental design while Earliest Uses has better coverage of time series analysis and stochastic processes. The Oxford English Dictionary often has excellent entries with apt quotations. Derek Bissell tells the stories of some individual terms.

• H. A. David (1995/1998/2001/2008) First (?) Occurrence of Common Terms in Mathematical Statistics, American Statistician (1995); First (?) Occurrence of Common Terms in Probability and Statistics—A Second List, with Corrections” ibid. (1998); Appendix B of H. A. David & A. W. F. Edwards (eds.) Annotated Readings in the History of Statistics (2001); the latest version is available here..
• Derek Bissell (1996) Statisticians Have a Word for It, Teaching Statistics, 18 (3), 87-89.

The Earliest Uses pages contain references to the secondary literature but it may be worth indicating some of the leading reference works. For the older terms—and most of the probability and statistics terms on the Earliest pages are pre-1960 and some pre-1900— the following histories are very useful

• Ian Hacking The Emergence of Probability, Cambridge, Cambridge University Press 1975.
• Stephen M Stigler, The History of Statistics: The Measurement of Uncertainty before 1900, Cambridge, MA: Belknap Press of Harvard University Press 1986.
• Anders Hald, A History of Probability and Statistics and their applications before 1750, New York: Wiley 1990.
• Anders Hald, A History of Mathematical Statistics from 1750 to 1930, New York: Wiley 1998.
• Helen M. Walker, Studies in the History of Statistical Method, with a Special Reference to Certain Educational Problems. Baltimore: Williams & Williams, 1929. Chapter VIII treats “The Origin of Certain Technical Terms used in Statistics.”

Encyclopedias are useful for more recent terms:

· Encyclopedia of Biostatistics (1998), Chichester: Wiley.

· The New Palgrave: A Dictionary of Economics (1987), London: Macmillan.

· Encyclopedia of Statistical Science (1982), New York: Wiley.

· International Encyclopedia of Statistics, (1978) New York: Free Press.

Dictionaries of Statistical terms usually contain some historical information. At present the leading one is

• Yadolah Dodge (ed.) Oxford Dictionary of Statistical Terms (2003), Oxford: Oxford University Press.

This has plenty of historical information and 60 pages of references but there seems to be no uniform policy about the use of references and most entries have no references.

For further information on sources, see Mathematical Words: Origins and Sources

Useful links

· My Figures from the History of Probability and Statistics has a sketch of the history of probability and statistics and notes on some of the key people.

· My Mathematical Words: Origins and Sources has examples from probability and statistics.

· Peter Lee’s Materials for the History of Statistics contains a wealth of information. Many of the classic works in probability and statistics can be found through the section on the Life and Work of Statisticians

· MacTutor has biographies of many of the mathematicians and statisticians who coined the terms and devised the symbols of probability and statistics.

· Kees Verduin’s A Short History of Probability and Statistics gives some key dates.

· The Earliest Uses entries do not generally contain definitions and Eastman & McColl's glossary may be a useful complement, at least for the more basic terms.

· The Maths Thesaurus (Connecting Mathematics) is another possible source for definitions.

· For brief essays on probability and statistics topics see the online encyclopaedias of mathematics, MathWorld, Encyclopaedia of Mathematics (a translation of the well-regarded Soviet work) and PlanetMath.

· The ISI Multilingual Glossary of Statistical Terms provides a bridge to other languages.

John Aldrich, University of Southampton, Southampton, UK. (home) March 2004. Most recent changes July 2011.