Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-19T21:23:56.842Z Has data issue: false hasContentIssue false
  • English
  • Français

The construction of limiting distributions of response probabilities

Published online by Cambridge University Press:  14 July 2016

G. S. Marliss  and
J. R. McGregor
G. S. Marliss
Affiliation:
Imperial College of Science and Technology, London
J. R. McGregor
Affiliation:
University of Alberta, Edmonton
Get access Rights & Permissions [Opens in a new window]

Extract

As stated elsewhere [9], the two experimenter-controlled events learning model of Bush and Mosteller [1] may be described by a Markov process X0,X1, ···satisfying the following conditions.

  1. (i) Xo has an arbitrary distribution on (0, 1).

  2. (ii) If Xn is given, then with probability π1 and with probability π2

  3. (ii)

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 757 - 766
Copyright
Copyright © Applied Probability Trust 1971 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bush, Robert R. and Mosteller, Frederick (1955) Stochastic Models for Learning. Wiley, New York.CrossRefGoogle Scholar
[2] Erdös, P. (1939) On a family of symmetric Bernoulli convolutions. Amer. J. Math. 61, 974–976.CrossRefGoogle Scholar
[3] Karlin, Samuel (1953) Some random walks arising in learning models I. Pacific J. Math. 3, 725–756.CrossRefGoogle Scholar
[4] Kemeny, J. G. and Snell, J. L. (1957) Markov processes in learning theory. Psychometrika 22, 221–230.CrossRefGoogle Scholar
[5] Kershner, R. and Wintner, A. (1935) On a family of symmetric Bernoulli convolutions. Amer. J. Math. 57, 546–547.CrossRefGoogle Scholar
[6] Kolmogorov, A. N. and Fomin, S. V. (1957) Elements of the Theory of Functions and Functional Analysis, Volume I, Metric and Normed Spaces. Graylock Press, Rochester, New York.Google Scholar
[7] Marliss, G. S. and Mcgregor, J. R. (1968) Symmetric limiting distributions of response probabilities. Psychometrika 33, 383–385.CrossRefGoogle ScholarPubMed
[8] Mcgregor, J. R. and Zidek, J. V. (1965). Limiting distributions of response probabilities. Ann. Math. Statist. 36, 706–707.CrossRefGoogle Scholar
[9] Mcgregor, J. R. and Zidek, J. V. (1965) A sequence of limiting distributions of response probabilities. Psychometrika 30, 491–497.CrossRefGoogle ScholarPubMed
[10] Norman, M. Frank (1966) Limiting distributions for some random walks arising in learning models. Ann. Math. Statist. 37, 393–405.CrossRefGoogle Scholar