A method of approximating percentile points of highly skewed, two parameter beta distributions

Abstract

An approximation formula is derived which provides a simplified and efficient method of calculating the O'th percentile point of a two parameter beta function when the two parameters are known. A specific application is presented by utilizing the formula to compute the lower 100(1-0!)% Bayesian confidence limit for the reliability of a component when the prior distribution of that reliability is known to be beta with parameters a' and b*. The posterior distribution is then determined by mission testing n items and recording the number of successes, s. This distribution is known to be beta with parameters a and b, where a = a' + s and b = b' + n - s. Therefore, the formula can be utilized to determine the Ofth percentile point of this posterior distribution which by definition is the lower 100(l-a)% confidence limit for the reliability of the component.