Re: [Help-gsl] gsl_ran_gaussian giving non-zero mean !

[Leo Razoumov]

On 2009-10-13, Sumesh P.T. <address@hidden> wrote:
> I am using gsl_ran_gaussian to generate a random number distribution
>  with a specified standard deviation. Surprisingly the mean of the
>  distribution is not zero !!! Can it be possible? The mean does not
>  fluctuate around zero, but rather tends to be with a positive
>  value....Is this expected? or my interpretation is wrong? Has anyone
>  tried this?
>  I am giving my program and result here:
>
>  ###########Program##########################3
>  #include <stdlib.h>
>  #include <math.h>
>  #include "concen.h"
>  #include <gsl/gsl_errno.h>
>  #include <gsl/gsl_matrix.h>
>  #include <gsl/gsl_odeiv.h>
>  #include <gsl/gsl_rng.h>
>  #include <gsl/gsl_randist.h>
>
>  int main() {
>  double y,sum=0.;
>  const gsl_rng_type * R;
>    gsl_rng * r;
>    gsl_rng_env_setup();
>    R = gsl_rng_default;
>    r = gsl_rng_alloc (R);
>    for(int i=1;i<=10000;i++) {
>      y = gsl_ran_gaussian(r,1.);
>      sum=sum+y;
>      printf("%f, %f, %f ,\n",y,sum,sum/i);
>    }
>  }
>  ##############################################
>  ##############################################
>  Last 10 values after calling it 10000 times
>  ------------------------------------------------------
>  random                 sum                    mean
>  0.806397,       130.966701,          0.013108 ,
>  -0.096531,      130.870170,         0.013097 ,
>  -0.440024,     130.430146,         0.013052 ,
>  0.482622,       130.912768,          0.013099 ,
>  0.798685,       131.711453,           0.013178 ,
>  1.904331,        133.615784,         0.013367 ,
>  0.124113,         133.739897,         0.013378 ,
>  -0.728447,       133.011450,         0.013304 ,
>  -1.790865,         131.220585,        0.013123 ,
>  -2.349805,          128.870779,       0.012887 ,
>
>  Both sum and mean are positive values with no fluctuations around
>  zero! Is not that surprising?
>
>  Thanks,
>  sumesh
>

I do not see any problem.
Your mean of 0.01 is consistent with your sample size. Mean converges
to zero rougly as 1/sqrt(N). Could you repeat you test with N=1000000
and N=10^8
To see fluctuations, please, change rng seed on each run.

--Leo--