Advertisement

Discrete First Passage Time Distribution for Describing Inequality among Individuals

  • Takemi Yanagimoto
Chapter

Abstract

The first passage time distribution of a random walk is extended in various ways to describe flexibly the distribution of time until transition. A random walk model, more generally a Markov chain model, provides us with a latent structure. On the other hand, the first passage time distribution describes observed data. Our special interest is in the possible causes of the distribution of time until transition. The latent structure model assumes two types of inequality as a cause; inequality of the ability among individuals and inequality due to an incidental position of an individual.

Keywords

Random Walk Markov Chain Model Random Walk Model Positive Mass Chess Player 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bartholomew, D.J. (1967), Stochastic Models for Social Processes, Wiley, New York.Google Scholar
  2. Feller, W. (1967), An Introduction to Probability Theory and its Applications, Vol. I (3rd ed.), Wiley, New York.Google Scholar
  3. Haight, F.A. (1961), “A distribution analogous to the Borrel-Tanner”, Biometrika, 48, 167173.Google Scholar
  4. Johnson, N.L., Kotz, S. and Kemp, A.W. (1992), Univariate Discrete Distributions - Second edition, Wiley, New York.Google Scholar
  5. Jorgensen, B. (1987), “Exponential dispersion model (with discussion)”, J. Roy. Statist. Soc., B, 49, 127–162.Google Scholar
  6. Kemp, C.D. and Kemp, A.W. (1968). “On a distribution associated with certain stochastic processes,” J. Roy. Statist. Soc., B, 30, 401–410.Google Scholar
  7. Mohanty, S.G. and Panny, W. (1990), “A discrete-time analogue of the M/M/1 queue and the transient solution: a geometric approach,” Sankhya, 52, 364–370.MathSciNetzbMATHGoogle Scholar
  8. Shimizu, K. and Yanagimoto, T. (1991), “The inverse trinomial distribution-an extension of the inverse binomial distribution (in Japanese with an English abstract),” Jap. J. Appl. Statist., 20, 89–96.CrossRefGoogle Scholar
  9. Takacs (1962), “A generalization of the ballot problem and its application in the theory of queues,” J. Amer. Statist. Assoc., 57, 327–337.MathSciNetzbMATHGoogle Scholar
  10. Whitmore, G.A. (1979), “ An inverse Gaussian model for labour turnover,” J. Roy. Statist. Soc., A, 142, 468–478.Google Scholar
  11. Whitmore, G.A. (1986), “First-passage-time models for duration data: regression structure and competing risk,” Statistician, 35, 207–219.MathSciNetCrossRefGoogle Scholar
  12. Whitmore, G.A. (1990), “Personal communication.”Google Scholar
  13. Yanagimoto, T. (1989), “The inverse binomial distributions as a statistical model,” Comm. In Statist-Theory Meth., 18, 3625–3633.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Takemi Yanagimoto
    • 1
  1. 1.Institute of Statistical MathematicsTokyo, 106Japan

Personalised recommendations