
MULTIVARIATE T RANDOM NUMBERName:
LET Y = <dist> RANDOM NUMBERS FOR I = 1 1 N LET Y = LOC + SCALE*Y Multivariate distributions, however, genrally require matrix operations. For this reason, random numbers for multivariate distributions each have their own unique syntax. Although you can generate P columns of t random numbers, this does take into account any correlation between the variables (i.e., they are independent). To generate an NxP matrix of t random numbers in Dataplot, you must specify a Px1 mean vector, a PxP variancecovariance matrix, and the desired degress of freedom (i.e., the shape parameter for the t distribution). The mean vector specifies the location parameters for each of the P columns. The diagonal of the variancecovariance matrix specifies the scale parameters of the P columns. A single value is specified for the degrees of freedom (i.e., all columns assume a common degrees of freedom).
<mu> <sigma> <nu> <n> where <mu> is a variable containing the desired location parameters; <sigma> is a matrix containing the desired variancecovariance matrix; <nu> is a number or parameter specifying the desired degrees of freedom; <n> is a number or parameter specifying the desired number of rows; and where <mat> is a matrix where the resulting multivariate normal random numbers are stored. Dataplot determines the number of columns to generate from the number of rows in the <mu> vector. Note that the number of rows in <mu> must equal the number of rows (and columns) in <sigma> and <sigma> must be a symmetric positivedefinite matrix (i.e., a value variancecovariance matrix).
READ MATRIX SIGMA 1 0.5 0.5 0.5 1 0.5 0.5 0.5 1 END OF DATA LET N = 500 LET NU = 500 LET M = MULTIVARIATE T RANDOM NUMBERS MU SIGMA NU N
RDMNOR was written by Charlie Reeves while he was a member of the NIST Statistical Engineering Division.
"Introduction to Matrix Computations", G. W. Stewart, Academic Press, Algorithm 3.9, p. 142.
dimension 100 columns . read matrix sigma 1.0 0.707107 0.0 0.0 0.0 0.707107 1.0 0.5 0.5 0.5 0.0 0.5 1.0 0.5 0.5 0.0 0.5 0.5 1.0 0.5 0.0 0.5 0.5 0.5 1.0 end of data . let mu = data 0 0 0 0 0 let n = 500 let nu = 3 . let m = multivariate normal random numbers mu sigma n . multiplot corner coordinates 0 0 100 100 multiplot 2 3 title automatic loop for k = 1 1 5 relative histogram m^k end of loop
Date created: 5/16/2003 