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

A. Moeini; Babak Abbasi; H. Mahlooji

doi:10.1080/03610918.2010.551012

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

A. Moeini, Babak Abbasi, H. Mahlooji

Research output: Contribution to journal › Article › Research › peer-review

11 Citations (Scopus)

Abstract

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 (λ_i, λ_i ≥ 0, i = 1,..., n) over a simplex in ℝ² (n ≥ 2), i.e., Σ_i=1 ⁿ λ_i = 1. In this article, first, conditional distribution of λ_i where Σ_i=1 ⁿ λ_i = 1 is derived and then inverse method is applied to generate random variables.

Original language	English
Pages (from-to)	685-693
Number of pages	9
Journal	Communications in Statistics - Simulation and Computation
Volume	40
Issue number	5
DOIs	https://doi.org/10.1080/03610918.2010.551012
Publication status	Published - May 2011
Externally published	Yes

Keywords

Conditional probability distribution
Simplex
Uniform random vector generation

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10.1080/03610918.2010.551012

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AU - Abbasi, Babak

AU - Mahlooji, H.

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AB - 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.

KW - Conditional probability distribution

KW - Simplex

KW - Uniform random vector generation

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ER -

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

Abstract

Keywords

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