) as a step function, one achieves the empirical distribution function of h at the point c. If g ( h ) = H i, one obtains the rth sample moment. If g ( h ) = h, that is, if h is a fixed point for g, then T represents an estimator of. ) is an arbitrary known function and H i = q ( x i ). Let h denote an objective function given by Д®fficiency of LHSMC Considers the case that x denotes an n-vectors random variable with p.d.f.In this case, the equal probability spaced values are 0. A 10-run LHS for three normalized variables (range ) with the uniform probability density function (p.d.f.) is listed below. Thus, for given values of N and n, there exist ( N ! ) n в€’ 1 possible interval combinations for an LHS. This set of Nn-tuples is the Latin hypercube sample. These N pairs are combined in a random manner with the N values of x 3 to form Nn-triplets, and so on, until a set of Nn-tuples is formed. The N values thus obtained for x 1 are paired in a random manner with the N values of x 2. One value from each interval is selected at random with respect to the probability density in the interval. The range of each variable is partitioned into N non-overlapping intervals on the basis of equal probability size 1 / N. As originally described, in the following manner, LHS operates to generate a sample size N from the x variables x 1, x 2, x 3. Moreover, the sample generation for correlated components with Gaussian distribution can be easily achieved. We will only consider the case where the components of x are independent or can be transformed into an independent base. The sampling region is partitioned into a specific manner by dividing the range of each component of x. The Latin Hypercube Sampling (LHS) is a type of stratified Monte Carlo (MC).

Multilevel latin hypercube sampling