On uniform design of experiments with restricted mixtures and generation of uniform distribution on some domains

Kai-Tai Fang*, Zhen-Hai Yang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

45 Citations (Scopus)

Abstract

In this paper we propose a new method, based on the conditional distribution method in Monte-Carlo methods, to generate the uniform distribution on the domain Tn(a,b)={(x1,...,xn):0≤a i≤xi≤bi≤1,0≤i≤n,x 1++xn=1}, where a=(a1,...,an) and b=(b1,...,bn). By this new method we can easily obtain uniform designs of experiments with mixtures, i.e., to generate a set of points that are uniformly scattered on the domain Tn(a,b). This approach can apply to generation of uniform distributions on various domains, such as convex polyhedron and simplex. These uniform distributions are useful in experimental design, reliability and optimization.

Original languageEnglish
Pages (from-to)113-120
Number of pages8
JournalStatistics and Probability Letters
Volume46
Issue number2
DOIs
Publication statusPublished - 15 Jan 2000
Externally publishedYes

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • 62E25
  • 62K15
  • Conditional distribution method
  • Experimental design
  • Monte-Carlo methods
  • Uniform design

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