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ESTIMATION OF PARAMETERS IN

THE BETA BINOMIAL MODEL

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RAM C. TRIPATHI^{1}, RAMESH C. GUPTA^{2} AND JOHN GURLAND^{3}

^{1} *Division of Mathematics, Computer Science and Statistics,*

The University of Texas, San Antonio, TX 78249, U.S.A.

^{2} *Department of Mathematics and Statistics, University of Maine,*

Orono, ME 04469-5752, U.S.A.

^{3} *Department of Statistics, University of Wisconsin, Madison, WI 53706, U.S.A.*
(Received July 8, 1991; revised September 28, 1993)

**Abstract.**
This paper contains some alternative methods
for estimating the parameters in the beta binomial and truncated
beta binomial models. These methods are compared with maximum
likelihood on the basis of Asymptotic Relative Efficiency (ARE).
For the beta binomial distribution a simple estimator based on
moments or ratios of factorial moments has high ARE for most of the
parameter space and it is an attractive and viable alternative to
computing the maximum likelihood estimator. It is also simpler to
compute than an estimator based on the mean and zeros, proposed by
Chatfield and Goodhart (1970, *Appl. Statist.*, **19**,
240-250), and has much higher ARE for most part of the parameter
space. For the truncated beta binomial, the simple estimator based
on two moment relations does not behave quite as well as for the BB
distribution, but a simple estimator based on two linear relations
involving the first three moments and the frequency of ``ones'' has
extremely high ARE. Some examples are provided to illustrate
the procedure for the two models.

*Key words and phrases*:
Maximum likelihood, minimum
chi-square, asymptotic relative efficiency, truncated beta binomial.

**Source**
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