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Conditional distribution inverse method in generating uniform random vectors over a simplex

Moeini, A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1080/03610918.2010.551012
  3. Abstract:
  4. Motivated by numerous applications in Monte Carlo techniques and as of late, in deriving non dominated solutions in multi-objective optimization problems, this article addresses generating uniform random variables (λi, λi ≥ 0, i = 1,..., n) over a simplex in ℝ2 (n ≥ 2), i.e., Σi=1 n λi = 1. In this article, first, conditional distribution of λi where Σi=1 n λi = 1 is derived and then inverse method is applied to generate random variables
  5. Keywords:
  6. Uniform random vector generation ; Conditional distribution ; Conditional probability distributions ; Inverse methods ; Monte Carlo techniques ; Multi-objective optimization problem ; Nondominated solutions ; Random vectors ; Simplex ; Uniform random variables ; Inverse problems ; Monte Carlo methods ; Multiobjective optimization ; Probability distributions ; Random variables
  7. Source: Communications in Statistics: Simulation and Computation ; Volume 40, Issue 5 , Dec , 2011 , Pages 685-693 ; 03610918 (ISSN)
  8. URL: http://www.tandfonline.com/doi/abs/10.1080/03610918.2010.551012