Monte Carlo Data Generation Techniques

SEPATH generates Monte Carlo data using pseudo-random number generation techniques. All random number procedures begin with generation of uniform random variates. The uniform random numbers are produced by a standard linear congruential generator. The generator creates the ith random integer via the formula

xi =  742938285xi-1(mod231-1) (186)

The integer can be transformed to a floating point number between zero and 1 by dividing by 231.

Uniform numbers are converted to simulated normal random numbers using Marsaglia's (1962) polar method. Independent normal random numbers are converted to multivariate normal numbers having a desired covariance structure by multiplying the p-variate vector by a Cholesky factor of the desired covariance matrix S.

Multivariate normal random variates are transformed into variates with desired (marginal) skewness and kurtosis using the technique of Vale and Maurelli (1983).