Estimation of a proportion using several independent samples of binomial mixtures

G. R. Wood; C. D. Lai; G. G. Qiao

doi:10.1111/j.1467-842X.2005.00407.x

Estimation of a proportion using several independent samples of binomial mixtures

G. R. Wood^*, C. D. Lai, G. G. Qiao

^*Corresponding author for this work

Research output: Contribution to journal › Article

4 Citations (Scopus)

Abstract

This paper considers a sequence of independent counts, with each count arising from a mixture of binomial distributions; the mixing distribution is fixed but the number of trials varies from count to count. In this common situation, an estimate of the underlying mean binomial proportion is needed. Two estimators are in general use: the arithmetic average and a weighted average of the observed proportions. Variances of the two estimators are compared and used to decide which estimator is preferred in a given context. The relative merits depend on the distribution of the proportions and the numbers of trials used.

Original language	English
Pages (from-to)	441-448
Number of pages	8
Journal	Australian and New Zealand Journal of Statistics
Volume	47
Issue number	4
DOIs	https://doi.org/10.1111/j.1467-842X.2005.00407.x
Publication status	Published - Dec 2005

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abstract = "This paper considers a sequence of independent counts, with each count arising from a mixture of binomial distributions; the mixing distribution is fixed but the number of trials varies from count to count. In this common situation, an estimate of the underlying mean binomial proportion is needed. Two estimators are in general use: the arithmetic average and a weighted average of the observed proportions. Variances of the two estimators are compared and used to decide which estimator is preferred in a given context. The relative merits depend on the distribution of the proportions and the numbers of trials used.",

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AB - This paper considers a sequence of independent counts, with each count arising from a mixture of binomial distributions; the mixing distribution is fixed but the number of trials varies from count to count. In this common situation, an estimate of the underlying mean binomial proportion is needed. Two estimators are in general use: the arithmetic average and a weighted average of the observed proportions. Variances of the two estimators are compared and used to decide which estimator is preferred in a given context. The relative merits depend on the distribution of the proportions and the numbers of trials used.

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