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.
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