A Functional Equation Analysis of Two Learning Models

Laveen Kanal

doi:10.1007/bf02289668

journal article Mar 01, 1962

A Functional Equation Analysis of Two Learning Models

Laveen Kanal

Psychometrika Vol. 27 No. 1 pp. 89-104 · Cambridge University Press (CUP)

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Abstract

One-absorbing barrier random walks arising from Luce's nonlinear beta model for learning and a linear commuting-operator model (called the alpha model) are considered. Functional equations for various statistics are derived from the branching processes defined by the two models. Solutions to general functional equations, satisfied by statistics of the alpha and beta models, are obtained. The methods presented have application to other learning models.

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References

15

[1]

Tatsuoka (1959)

[2]

Lamperti "Some asymptotic properties of Luce's beta learning model" Psychometrika (1960) 10.1007/bf02289727

[3]

Adams "Linearq-difference equations" Bull. Amer. math. Soc. (1931) 10.1090/s0002-9904-1931-05162-4

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Fey "Investigation of some mathematical models for learning" J. exp. Psychol. (1961) 10.1037/h0046472

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Adams "On the linear ordinaryq-difference equation" Ann. Math. (1929) 10.2307/1968274

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Bush (1959)

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Bush (1959)

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Bush (1959)

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[11] Kanal, L. Analysis of some stochastic process arising from a learning model. Unpublished doctoral thesis, Univ. Penn., 1960.

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Bellman (1952)

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Bush (1955) 10.1037/14496-000

[12]

Luce (1959)

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[14] Tatsuoka, M. Asymptotic mean and variance of number of errors for the beta model. Unpublished memo. PC-11, 1958.

[14]

Bush (1959)

[15]

Bush (1960)

Metrics

6

Citations

15

References

Details

Published: Mar 01, 1962
Vol/Issue: 27(1)
Pages: 89-104
License: View

Authors

L

Laveen Kanal

General Dynamics/Electronics

Cite This Article

Laveen Kanal (1962). A Functional Equation Analysis of Two Learning Models. Psychometrika, 27(1), 89-104. https://doi.org/10.1007/bf02289668

A Functional Equation Analysis of Two Learning Models

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