INEQUALITIES AND TOLERANCE LIMITS FOR S-ORDERED DISTRIBUTIONS
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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Define F subscript s G F subscript r G if F and G have the same median, say the origin and G superscript -1 Fx is concave-convex about the origin G superscript -1 Fxx is increasing decreasing in x positive negative. Conservative tolerance limits are derived for distributions which are s-ordered with respect to the Laplace distribution. These are especially reasonable for mensuration data. In addition, many inequalities concerning combinations of order statistics are obtained. These results are useful in robustness studies of tolerance limits, estimates and statistical tests derived for specified distributions such as the normal distribution. Some examples are given.
- Statistics and Probability