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ESTIMATION OF A PROPORTION USING SEVERAL INDEPENDENT SAMPLES OF BINOMIAL MIXTURES
Author(s) -
Wood G.R.,
Lai C.D.,
Qiao C.G.
Publication year - 2005
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2005.00407.x
Subject(s) - mathematics , estimator , statistics , negative binomial distribution , count data , binomial distribution , context (archaeology) , binomial (polynomial) , negative multinomial distribution , econometrics , beta binomial distribution , poisson distribution , paleontology , biology
Summary 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.