The Annals of Mathematical Statistics

Limiting Distributions Associated with Certain Stochastic Learning Models

J. R. McGregor and Y. Y. Hui

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Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 33, Number 4 (1962), 1281-1285.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177704360

Digital Object Identifier
doi:10.1214/aoms/1177704360

Mathematical Reviews number (MathSciNet)
MR142172

Zentralblatt MATH identifier
0124.34201

JSTOR
links.jstor.org

Citation

McGregor, J. R.; Hui, Y. Y. Limiting Distributions Associated with Certain Stochastic Learning Models. Ann. Math. Statist. 33 (1962), no. 4, 1281--1285. doi:10.1214/aoms/1177704360. https://projecteuclid.org/euclid.aoms/1177704360


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