V102 Pair of Random Numbers in Normal Distribution

OBSOLETE

Please note that this routine has been obsoleted in CNL 215. Users are advised not to use it any longer and to replace it in older programs. No maintenance for it will take place and it will eventually disappear.
Suggested replacement: CORSET (V122)

NORMCO generates two Gaussian distributed pseudo random numbers a and b with means $m$_a,m_b , standard deviations $\sigma$_a,σ_b

and correlation coefficient $\rho$ predefined by the user.

Structure:

SUBROUTINE subprogram
User Entry Names: NORMCO
External References: RNDM (V104)

Usage:

    CALL NORMCO(A,B,UA,UB,SIGMAA,SIGMAB,RHO)

A,B

( REAL) The two random numbers a and b.

UA

( REAL) The desired mean $m$_a .

UB

( REAL) The desired mean $m$_b .

SIGMAA

( REAL) The desired standard deviation $\sigma$_a .

SIGMAB

( REAL) The desired standard deviation $\sigma$_b .

RHO

( REAL) The desired correlation coefficient $\rho$

between A and B.

Method:

The routine generates two normal deviates

$a$	$=$	$m$a+σa-2lny&sp;( 1-ρ2cos(2πx)+ρsin(2πx) )
$b$	$=$	$m$b+ρb-2lnysin(2πx)

with each execution. x,y are random numbers, uniformly distributed in the interval (0,1) and obtained from RNDM (V104).

Notes:

For $m$_a,m_b=0 , $\sigma$_a,σ_b=1 , $\rho =0$ use RANNOR (V100).

References:

1. B. Jansson, BIT 4 (1964).

V103