Conditional Distribution Inverse Method in Generating Uniform Random Vectors Over a Simplex

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., . In this article, first, conditional distribution of λ i where is derived and then inverse method is applied to generate random variables.