Re: (MATH-STAST) Generate random numbers

[Tuan V Nguyen <t.nguyen@garvan.unsw.edu.au>]

Hi  Long & friends,

>	Dear friends
>
>	Could anyone can help me in generating pairs of
>zero-correlated, standard normally distributed numbers.
>The recommended method is IMSL routine GGNPM - which I do not
>know either.
>Thanks in advance.

        The algorithm for generating two random variables X and Y, each with
mean MX, MY and standard deviattion SX and SY and correlation R is as follows:

        1. generate a normal random variable with mean=0 and variance=1, let
it be z1;

        2. generate another normal random variable with mean=0 and
variance=1, let it be z2.

        3. create a variable X = MX + SX*Z1
           create a variable Y = MY + R*SY*Z1 + SY*sqrt(1-R**2) + Z2;

        4. The correlation between X and Y should be approx R.

        You can substitute MX=MY=0, SX=SY=1 and R=0 for the above
formulation and go!

        Here are 50 observations with approx. 0 correlation and eachwith
mean 0 and variance of 1.
                                  X           Y

                               0.46284     1.93287
                              -0.59628    -0.38840
                               0.47273    -1.06919
                               1.13667    -0.42674
                              -1.52205     1.19419
                               1.40778     0.04346
                              -1.71348     1.09803
                               0.69807     0.31912
                               1.28487     1.85487
                               0.25709    -0.88396
                              -0.36480    -0.26223
                              -0.73485    -0.49349
                              -0.37251     0.23331
                              -0.71049     1.33718
                              -0.35243    -0.64554
                              -0.81009    -1.51166
                               0.85254     0.33523
                               2.04217     0.67813
                               0.04086    -0.82262
                               0.69284    -2.60963
                               1.10545    -1.43916
                              -1.48103     1.13937
                              -0.03113    -0.92592
                              -0.27095    -0.59528
                               0.14431     0.48531
                               0.87341     0.35754
                               1.04104     0.83077
                              -0.56205    -0.06848
                              -0.09275     1.22794
                               1.34662     0.09265
                               0.34870    -0.29748
                               1.84143     1.09846
                               0.27511    -0.82314
                               1.86124    -0.01651
                              -0.17230     0.42690
                               0.95681     1.06141
                              -1.18143    -1.01295
                              -0.58743     0.69852
                              -1.13559     1.11143
                               0.03381     1.84566
                               0.03313     0.76189
                               1.77009    -0.12085
                              -2.91779    -0.27002
                              -0.24536     0.55432
                              -1.01339    -0.48828
                              -0.25248     0.19036
                              -1.19737     0.39530
                              -0.03591    -0.49682
                               0.61053     0.67247
                              -1.12823    -0.52824



        Hope it helps.

        Tuan