INEQUALITIES AND TOLERANCE LIMITS FOR S-ORDERED DISTRIBUTIONS

Abstract

Define F < (subscript s) G F < (subscript r) G if F and G have the same median, say the origin and G (superscript -1) F(x) is concave-convex about the origin (G (superscript -1) F(x)/x 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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1966
Accession Number
AD0654154

Entities

People

  • Michael J. Lawrence

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Contractors
  • Contracts
  • Data Science
  • Distribution Functions
  • Information Science
  • Normal Distribution
  • Observation
  • Order Statistics
  • Probability
  • Random Variables
  • Sequences
  • Skewness
  • Statistical Tests
  • Statistics
  • Theorems
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Mathematics or Statistics
  • Statistical inference.