MNSIMUL <corr_file>,<msn_file>,<data_file>,N,<ind>
simulates multivariate normal distribution by generating N obser-
vations according to a given CORR file and MSN file (of means and
std.devs).
The simulated observations will be saved in <data_file>. If
<data_file> already exists, its previous structure and contents
will be destroyed.
If <msn_file> is given as *, means are assumed to be =0 and
std.devs=1, i.e. standardized data will be produced.
When <ind> is 0, the covariance matrix S is computed from the given
correlation matrix and standard deviations. Then S is decomposed
into form S=CC' by spectral decomposition. The data values are
generated by the formula X=C*U+M where U is multivariate N(0,I)
and M is the vector of means.
C is saved as a matrix file MNCOEFF.M on the temporary disk (tempdisk)
of Survo. Similarly, M (if given) is saved as MNMEAN.M .
Also a new data file <data_file> is created.
After these preparations MNSIMUL generates the N observations.
When <ind> is 1, the above preparations are omitted and N observations
are generated directly by using ready-made MNCOEFF.M and MNMEAN.M files.
Thus in simulation experiments where many samples from the same
multivariate normal distribution are required, the first sample
must be created by setting <ind> to 0.
Samples #2, #3, etc. can then be generated more quickly by setting <ind> to 1.
For each sample, a different seed for (pseudo)random numbers must be used.
The random number generator and its seed number is selected by specification
RND=rand(1041994), for example. Default is RND=rand(123456789).
Also INSEED and OUTSEED specifications are available (see RAND?).
The normal random deviates are computed by default by the Box-Müller method.
By specification TRANSFORM=PROBIT, an approximation of the inverse normal
distribution is used instead. By this option (which is slightly slower)
MNSIMUL generates exactly same values as the /MNSIMUL sucro.
The names of variables in <data_file> are the row labels of <corr_file>.
By default each variable is of the numerical type 4.
The types can be changed by TYPES=<1,2,4 or 8>
or by TYPES=<name_of_data_file>.
In the latter case the types are selected according to variables
in another data file.
The size of the data file is minimal, i.e. no space for additional variables
is reserved.
However, by NEWSPACE=<#_of_additional_bytes>,<#_of_additional_variables>
such additional space can be created for each observation.
Another form of MNSIMUL is
MNSIMUL <cov>,-,<data_file>,N,<ind>
where <cov> is the covariance matrix of the distribution to be simulated.
In this case it is assumed that means will be 0.
1 = More information on additional multivariate operations
M = More information on multivariate analysis
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