Simple, Efficient Closed-Form Approximations for Beta Percentiles, Exponential Prediction Intervals and Confidence Bounds on Exponential and Binomial Parameters.
ROCKWELL INTERNATIONAL CORP CANOGA PARK CALIF ROCKETDYNE DIV
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The use of Patnaiks 1949 Chi-square approximation to the non-central Chi-square distribution and the Wilson-Hilferty 1931 transformation of Chi-square to approximate normality are explored herein as a simple, efficient means of finding one-or-two-order statistic confidence bounds on parameters of the one- and two-parameter negative exponential distributions. Such methods can be used when it is known that r of n sample items, r or n, have failed during a life test, but the times of some early failures are not known exactly. An important implication of the result applying to approximate confidence bounds on the mean of an exponential distribution from a single order statistic is that of obtaining simple-closed-form approximations to percentiles of the Beta distribution with integer parameters. It is shown that a generalization of the approximation applies to Beta variates with noninteger parameters. Modified author abstract
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems