Probability and Statistical Models

  • David Ruppert
Part of the Springer Texts in Statistics book series (STS)


It is assumed that the reader is already at least somewhat familiar with the basics of probability and statistics. The goals of this chapter are to
  1. 1.

    review these basics;

  2. 2.

    discuss more advanced; topics needed in our empirical study of financial markets data such as random vectors, covariance matrices, best linear prediction, heavy-tailed distributions, maximum likelihood estimation, and likelihood ratio tests;

  3. 3.

    provide glimpses of how probability and statistics are applied to finance problems in this book; and

  4. 4.

    introduce notation that is used throughout the book.



Probability Density Function Cumulative Distribution Function Pareto Distribution Normal Probability Plot Tail Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alexander, C. (2001) Market Models: A Guide to Financial Data Analysis, Wiley, Chichester.Google Scholar
  2. Bernardo, J. M. and Smith, A. F. M. (1994) Bayesian Theory, Wiley, Chichester.CrossRefMATHGoogle Scholar
  3. Box, G. E. P. and Tiao, G. C. (1973) Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading, MA.MATHGoogle Scholar
  4. Casella, G. and Berger, R. L. (2002) Statistical Inference, 2nd Ed., Thomson Learning, Pacific Grove, CA.Google Scholar
  5. Congdon, P. (2001) Bayesian Statistical Modelling, Wiley, Chichester. Congdon, P. (2003) Applied Bayesian Modelling, Wiley, Chichester.Google Scholar
  6. Delwiche, L. D. and Slaughter, S. J. (1998) The Little SAS Book: A Primer, 2nd Ed., SAS Publishing, Cary, N. C.Google Scholar
  7. Drees, H., de Haan, L., and Resnick, S. (2000) How to make a Hill plot, The Annals of Statistics, 28, 254–274.MathSciNetCrossRefMATHGoogle Scholar
  8. Edwards, W. (1982) Conservatism in human information processing. In Judgement Under Uncertainty: Heuristics and Biases, edited by Kahneman, D., Slovic, P., and Tversky, A., Cambridge University Press, New York.Google Scholar
  9. Evans, M., Hastings, N., and Peacock, B. (1993) Statistical Distributions, 2nd Ed., Wiley, New York.MATHGoogle Scholar
  10. Fama, E. (1965) The behavior of stock market prices, Journal of Business, 38, 34–105.CrossRefGoogle Scholar
  11. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1995) Bayesian Data Analysis, Chapman & Hall, London.MATHGoogle Scholar
  12. Gourieroux, C. and Jasiak, J. (2001) Financial Econometrics, Princeton University Press, Princeton, NJ.MATHGoogle Scholar
  13. Hanselman, D. and Littlefield, B. R. (2000) Mastering MATLAB 6, Prentice-Hall, Upper Saddle River, NJ.Google Scholar
  14. Johnson, N. L., Kotz, S., and Balakrishnan, N., (1994) Continuous Univariate Distributions, Vol. 1, 2nd Ed., Wiley, New York.MATHGoogle Scholar
  15. Johnson, N. L., Kotz, S., and Balakrishnan, N. (1995) Continuous Univariate Distributions, Vol. 2, 2nd Ed., Wiley, New York.MATHGoogle Scholar
  16. Johnson, N. L., Kotz, S., and Kemp, A. W. (1993) Discrete Univariate Distributions, 2nd Ed., Wiley, New York.Google Scholar
  17. Mandelbrot, B. (1963) The variation of certain speculative prices, Journal of Business, 36, 394–419.CrossRefGoogle Scholar
  18. Resnick, S. I. (2001) Modeling Data Networks, School of Operations Research and Industrial Engineering, Cornell University, Technical Report #1345.Google Scholar
  19. Self, S. G. and Liang, K. Y. (1987) Asymptotic properties of maximum likeli-hood estimators and likelihood ratio tests under non-standard conditions. Journal of the American Statistical Association, 82, 605–610.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • David Ruppert
    • 1
  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

Personalised recommendations