The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Random Variables

  • I. Richard Savage
Reference work entry


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 is a preview of subscription content, log in to check access.


  1. 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.Google Scholar
  2. Anderson, T.W. 1984. An introduction to multivariate statistical analysis, 2nd ed. NewYork: Wiley. 1972.Google Scholar
  3. Ash, R.B. 1972. Real analysis and probability. New York: Academic.Google Scholar
  4. Barlow, R.E., and F. Proschan. 1975. Statistical theory of reliability and life testing probability models. New York: Holt, Rinehart and Winston.Google Scholar
  5. Chow, Y.S., and H. Teicher. 1978. Probability theory: Independence interchangeability, martingales. New York: Springer.CrossRefGoogle Scholar
  6. David, H.A. 1981. Order statistics, 2nd ed. New York: Wiley.Google Scholar
  7. Greenwood, J.A., and H.O. Hartley. 1962. Guide to tables in mathematical statistics. Princeton: Princeton University Press.Google Scholar
  8. Johnson, N.L. 1969. Distributions in statistics: Discrete distributions. Boston: Houghton Mifflin, chs 1–11.Google Scholar
  9. Johnson, N.L. 1970a. Continuous distributions, vol. 1. Boston: Houghton Mifflin, chs 12–24.Google Scholar
  10. Johnson, N.L. 1970b. Continuous distributions, vol. 2. Boston: Houghton Mifflin, chs 22–33.Google Scholar
  11. Johnson, N.L. 1972. Continuous multivariate distributions. New York: Wiley, chs 34–42.Google Scholar
  12. Karlin, S., and H.M. Taylor. 1975. A first course in stochastic processes, 2nd ed. New York: Academic.Google Scholar
  13. Lamperti, J. 1966. Probability: A survey of mathematical theory. New York: W.A. Benjamin.Google Scholar
  14. Lukacs, E. 1970. Characteristic functions, 2nd ed. New York: Hafner Publishing.Google Scholar
  15. Pollard, D. 1984. Convergence of stochastic processes. New York: Springer.CrossRefGoogle Scholar
  16. Rao, C. 1973. Linear statistical inference and its applications, 2nd ed. New York: Wiley.CrossRefGoogle Scholar
  17. Serfling, R.J. 1980. Approximation theorems of mathematical statistics. New York: Wiley.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • I. Richard Savage
    • 1
  1. 1.