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December, 1962 Limiting Distributions Associated with Certain Stochastic Learning Models
J. R. McGregor, Y. Y. Hui
Ann. Math. Statist. 33(4): 1281-1285 (December, 1962). DOI: 10.1214/aoms/1177704360


The work of Bush and Mosteller [1] on stochastic learning models leads to certain limiting distributions of response probabilities which are of a somewhat different character from those commonly encountered in mathematical statistics. These authors have derived many useful relations between the moments of the distributions but, in deducing the general nature of the distributions themselves, they have relied chiefly on Monte Carlo methods. In the present paper, we consider the two experimenter-controlled events model and, in the "equal alpha" case, derive limiting distributions for certain special cases by inverting the solution of a moment generating functional equation.


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J. R. McGregor. Y. Y. Hui. "Limiting Distributions Associated with Certain Stochastic Learning Models." Ann. Math. Statist. 33 (4) 1281 - 1285, December, 1962.


Published: December, 1962
First available in Project Euclid: 27 April 2007

zbMATH: 0124.34201
MathSciNet: MR142172
Digital Object Identifier: 10.1214/aoms/1177704360

Rights: Copyright © 1962 Institute of Mathematical Statistics

Vol.33 • No. 4 • December, 1962
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