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Randy Silvers
03/13/07 01:11am

I've run into a bit of an oddity and I'm not sure of the cause though the repair is easy. I have a function which requires in the denominator the product:

ndcdf[beta*x] * (1 - ndcdf[beta*x])

where ndcdf is the CDF of the Standard Normal distribution.

The computed value is fine except when beta*x is large and positive. For values exceeding about 8.5, the result is ComplexInfinity.

When beta*x is large in magnitude but negative, the result is positive and exceedingly large, as it should be. This contrasts with the value of ComplexInfiinty, when beta*x is large and positive. The fix is clearly to use:

ndcdf[-Abs[beta*x]] * (1 - ndcdf[-Abs[beta*x]])

But, why is the kernel producing Complex Infinity here? The function is symmetric about x=0, so it should be the same for positive or negative, and should not vanish.

For example:

lst=Table[i,{i,12}]; llst=Join[-1*Reverse[lst],{0},lst]

then

Map[1/(ndcdf[#](1-ndcdf[#]))&,llst]

shows the symmetry for for integer values 8 or less, but ComplexInfinity for values greater than 8 and positive.

URL: sirandol@deakin.edu.au,

Thread 'Normal Distribution CDF' is now CLOSED
Author Date Posted
Normal Distribution CDF Randy Silvers 03/13/07 01:11am
Re: Normal Distribution CDF yehuda ben-s... 03/13/07 10:45am
Re: Re: Normal Distribution CDF Randy Silvers 03/14/07 08:02am
Re: Normal Distribution CDF yehuda ben-s... 03/15/07 11:36am
Re: Normal Distribution CDF yehuda ben-s... 03/15/07 11:48am
Re: Re: Normal Distribution CDF Randy Silvers 03/31/07 00:02am
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