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March, 1973 Statistical Inference in Bernoulli Trials with Dependence
Jerome Klotz
Ann. Statist. 1(2): 373-379 (March, 1973). DOI: 10.1214/aos/1176342377

Abstract

A model for Bernoulli trials with Markov dependence is developed which possesses the usual frequency parameter $p = P\lbrack X_i = 1\rbrack$ and an additional dependence parameter $\lambda = P\lbrack X_i = 1 \mid X_{i-1} = 1\rbrack$. Sufficient statistics for the model with $p$ and $\lambda$ unknown are found and an exact closed form expression for their small sample joint distribution is given. Large sample distribution theory is also given and small sample variances compared with large sample approximations. Easily computed estimators of $p$ and $\lambda$ are recommended and shown to be asymptotically efficient. With $p$ unknown the u.m.p. unbiased test of independence is noted to be the run test. An application to a rainfall example is given.

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Jerome Klotz. "Statistical Inference in Bernoulli Trials with Dependence." Ann. Statist. 1 (2) 373 - 379, March, 1973. https://doi.org/10.1214/aos/1176342377

Information

Published: March, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0256.62029
MathSciNet: MR381103
Digital Object Identifier: 10.1214/aos/1176342377

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 2 • March, 1973
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