Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0; 1) random variables (i.e., continuous random variables distributed uniformly over the interval (0; 1)). These random numbers are then transformed as needed...

This paper proposes a probabilistic load flow (PLF) methodology using uniform design sampling (UDS). The correlation between input random variables has been taken into consideration. The random numbers of random variables uniformly distributed in (0,1) are generated by UDS, and subsequently converted into random numbers of input random variables with desired marginal distributions by marginal t...

Abstract Motivated by the random covering problem and study of Dirichlet uniform approximable numbers, we investigate problem. Precisely, consider an i.i.d. sequence $\omega =(\omega _n)_{n\geq 1}$ uniformly distributed on unit circle $\mathbb{T}$ a $(r_n)_{n\geq positive real numbers with limit $0$. We size set $$\begin{align*} & {\operatorname{{{\mathcal{U}}}}} (\omega):=\{y\in \mathbb{T}...

A recently developed Centroidal Voronoi Tessellation (CVT) sampling method is investigated here to assess its suitability for use in statistical sampling applications. CVT efficiently generates a highly uniform distribution of sample points over arbitrarily shaped M-Dimensional parameter spaces. On several 2-D test problems CVT has recently been found to provide exceedingly effective and effici...