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Exact, Smallest Confidence Interval generation

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An iterative method is used to generate the smallest possible confidence intervals for the beta prior distribution. The process is iterative, so its drawback is increased processing time. The algorithm which I've developed combines Newton's Method and Bisection to converge upon the solution as quickly as possible.

The figure demonstrates exactly how these confidence intervals are obtained. The routine betaCI endeavors to find a value for ysuch that the two values x_L and x_H (where $y = {\rmbeta}(x_L,a,b) = {\rm beta}(x_H,a,b)$ ) create bounds for an exact CI level confidence interval.

Murray Todd Williams

1998-08-14