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 alpha th percentile point of a two parameter beta function when the two parameters are known. A specific application is presented by using the formula to compute the lower 100(1-alpha)% 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 alpha th percentile point of this posterior distribution which by definition is the lower 100(1-alpha)% confidence limit for the reliability of the component. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1971
- Accession Number
- AD0721232
Entities
People
- Thornton Boyd
Organizations
- Naval Postgraduate School