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Description:
The routine returns the variances and covariances of
the order statistics, assuming an initial (pre-ordered) normal distribution of mean 0 and standard
deviation 1. The routine returns all variance/covariances in an array with the terms vectorised - that is
following on after each row. This uses the symmetric nature of the matrix to compress the data
storage, but remember to double the covariance components if summing in quadrature. The variances
Invocation
CALL KPG1_ORVAR( NSET, NBIG, PP, VEC, STATUS )
Arguments
NSET = INTEGER (Given)
Number of members in ordered set.
NBIG =
INTEGER (Given)
Maximum number of entries in covariance array row. equal to
NSET(NSET1)/2).
PP( NSET ) = DOUBLE PRECISION (Given)
Workspace for storing expected values
of order statistics.
VEC( NBIG, NSET ) = DOUBLE PRECISION (Returned)
The
upper triangles of the nset by nset variance-covariance matrix packed by columns.
Each triangle is packed into a single row. For each row element Vij is stored in
VEC(ij(j-1)/2),
for 1=i=j=nset.
STATUS = INTEGER (Given and Returned)
The global status.
Notes:
-
Data is returned as above to save on repeated calls (which are too slow). To get the actual variance of
the data of order n you need to sum all the variances and twice the covariances and use these to
modify the actual variance of the (unordered) data.
-
It is assumed that NSET cannot be any larger than MXVAL.
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