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The Asymptotic Distribution for the Two-Absorbing-Barrier Beta Model

Published online by Cambridge University Press:  01 January 2025

Laveen Kanal
Laveen Kanal*
Affiliation:
General Dynamics/Electronics, Rochester, New York
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Abstract

For the two-absorbing-barrier specialization of Luce's beta learning model, the asymptotic distribution of the response probability has all its density at p = 0 and p = 1. The functional equation for the amount of the density at p = 1 is investigated in this paper.

Type
Original Paper
Information
Psychometrika , Volume 27 , Issue 1 , March 1962 , pp. 105 - 109
Copyright
Copyright © 1962 The Psychometric Society

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Footnotes

*

Abstracted from a portion of the author's doctoral dissertation, University of Pennsylvania, June 1960. The author is indebted to Prof. B. Epstein and to Prof. Robert R. Bush, his dissertation supervisor, for the valuable help and encouragement received from them.

†

Formerly at the Moore School of Electrical Engineering, University of Pennsyvania, Philadelphia, Pa. The author is grateful to the Moore School for the support extended to him during his doctoral studies. He also wishes to thank D. Parkhill and N. Finkelstein of General Dynamics for their encouragement of his work.

References

Bellman, R. On a certain class of functional equations. In Harris, T. E., Bellman, R., and Shapiro, H. (Eds.), Functional equations occurring in decision processes, Santa Monica, Calif.: Rand Corp., 1952.Google Scholar
Bush, R. R. Some properties of Luce's beta model for learning. In Arrow, K. J., Karlin, S., and Suppes, P. (Eds.), Proceedings of the First Stanford Symposium on mathematical methods in the social sciences, Stanford, Calif.: Stanford Univ. Press, 1960.Google Scholar
Kanal, L. A functional equation analysis for two learning models. Psychometrika, 1962, 27, 89–104.CrossRefGoogle Scholar
Kanal, L. Analysis of some stochastic processes arising from a learning model. Unpublished doctoral thesis, Univ. Pennsylvania, 1960.Google Scholar
Luce, R. D. Individual choice behavior, New York: Wiley, 1959.Google Scholar