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# lhsnorm

Latin hypercube sample from normal distribution

## Syntax

X = lhsnorm(mu,sigma,n)
X = lhsnorm(mu,sigma,n,flag)
[X,Z] = lhsnorm(...)

## Description

X = lhsnorm(mu,sigma,n) returns an n-by-p matrix, X, containing a latin hypercube sample of size n from a p-dimensional multivariate normal distribution with mean vector, mu, and covariance matrix, sigma.

X is similar to a random sample from the multivariate normal distribution, but the marginal distribution of each column is adjusted so that its sample marginal distribution is close to its theoretical normal distribution.

X = lhsnorm(mu,sigma,n,flag) controls the amount of smoothing in the sample. If flag is 'off', each column has points equally spaced on the probability scale. In other words, each column is a permutation of the values G(0.5/n), G(1.5/n), ..., G(1-0.5/n) where G is the inverse normal cumulative distribution for that column's marginal distribution. If flag is 'on' (the default), each column has points uniformly distributed on the probability scale. For example, in place of 0.5/n you use a value having a uniform distribution on the interval (0/n,1/n).

[X,Z] = lhsnorm(...) also returns Z, the original multivariate normal sample before the marginals are adjusted to obtain X.

## References

[1] Stein, M. "Large sample properties of simulations using latin hypercube sampling." Technometrics. Vol. 29, No. 2, 1987, pp. 143–151. Correction, Vol. 32, p. 367.