CCG_ORVAR - Returns the variances and covariances of the order statistics from n to 1, assuming an initially normal distribution

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

• covariances are returned for all statistics from n to 1. The special case of n = 1 returns the variance of 2/pi (median).

Invocation:

CALL CCG_ORVAR( EL, NBIG, PP, VEC, MATRIX, STATUS )

Arguments:

EL = INTEGER (Given)

Number of members in ordered set.

NBIG = INTEGER (Given)

Maximum number of entries in covariance array row. equal to EL$*$(EL$+$1)/2).

PP( EL ) = DOUBLE PRECISION (Given)

Workspace for storing expected values of order statistics.

VEC( NBIG, EL ) = 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(i$+$j$*$(j-1)/2), for 1 $<$= i $<$= j $<$= nset.

MATRIX( EL, EL ) = DOUBLE PRECISION (Returned)

Work space.

STATUS = INTEGER (Given and Returned)

The global status.

Notes:

• Data are returned as above to save on repeated calls (which are too slow). To obtain 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.