Abstract
Scientific statements often have a probabilistic element, for example, ‘In population Ω the distribution of individual income, I, can be approximated by a log-normal distribution’. The formal interpretation of this statement requires a moderate amount of structure, such as,
This chapter was originally published in The New Palgrave: A Dictionary of Economics, 1st edition, 1987. Edited by John Eatwell, Murray Milgate and Peter Newman
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Bibliography
Note. Some of the criteria used in selecting the references were clarity, availability and completeness. The Johnson and Kotz volumes are a storehouse of information about specific random variables, and Greenwood and Hartley gives extensive detail on available printed tables. The best entry to the current literature on random variables or other statistical-probabilistic topics is the Current Index to Statistics (published by the American Statistical Association and the Institute of Mathematical Statistics, 1984, volume 10, also available electronically as MathScience produced by the American Mathematics Society) which is a key-word, permuted-title index. Barlow and Proschan, David, Lukacs and Pollard are monographs on specialized topics. Comprehensive views of broad areas are given by Anderson, Chow and Teicher, Rao and Serfling. Ash gives a detailed mathematical setting for probability theory, and Lamperti quickly shows the power of the theory.
Anderson, T.W. 1984. An introduction to multivariate statistical analysis, 2nd ed. NewYork: Wiley. 1972.
Ash, R.B. 1972. Real analysis and probability. New York: Academic.
Barlow, R.E., and F. Proschan. 1975. Statistical theory of reliability and life testing probability models. New York: Holt, Rinehart and Winston.
Chow, Y.S., and H. Teicher. 1978. Probability theory: Independence interchangeability, martingales. New York: Springer.
David, H.A. 1981. Order statistics, 2nd ed. New York: Wiley.
Greenwood, J.A., and H.O. Hartley. 1962. Guide to tables in mathematical statistics. Princeton: Princeton University Press.
Johnson, N.L. 1969. Distributions in statistics: Discrete distributions. Boston: Houghton Mifflin, chs 1–11.
Johnson, N.L. 1970a. Continuous distributions, vol. 1. Boston: Houghton Mifflin, chs 12–24.
Johnson, N.L. 1970b. Continuous distributions, vol. 2. Boston: Houghton Mifflin, chs 22–33.
Johnson, N.L. 1972. Continuous multivariate distributions. New York: Wiley, chs 34–42.
Karlin, S., and H.M. Taylor. 1975. A first course in stochastic processes, 2nd ed. New York: Academic.
Lamperti, J. 1966. Probability: A survey of mathematical theory. New York: W.A. Benjamin.
Lukacs, E. 1970. Characteristic functions, 2nd ed. New York: Hafner Publishing.
Pollard, D. 1984. Convergence of stochastic processes. New York: Springer.
Rao, C. 1973. Linear statistical inference and its applications, 2nd ed. New York: Wiley.
Serfling, R.J. 1980. Approximation theorems of mathematical statistics. New York: Wiley.
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Savage, I.R. (1987). Random Variables. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_1476-1
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DOI: https://doi.org/10.1057/978-1-349-95121-5_1476-1
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