From octave-sources-request at bevo dot che dot wisc dot edu Mon Sep 23 08:51:58 2002
Subject: NORMPDF, NORMCDF, NORMINV (Re: normal distribution at v==0)
From: Schloegl Alois <alois dot schloegl at tugraz dot at>
To: octave-sources at bevo dot che dot wisc dot edu
Cc: Paul Kienzle <pkienzle at jazz dot ncnr dot nist dot gov>, bug-octave@bevo.che.wisc.edu,    deego@glue.umd.edu, edd@debian.org
Date: Mon, 23 Sep 2002 05:37:18 -0500


> 
> If there is a singularity X0 in a piecewise continous function f(X), we
> can 
> obtain the limes towards the singular point. 
>  
>    lim v->+0: normpdf(x,m,v) == inf     for x == m
>    lim v->+0: normpdf(x,m,v) == 0       for x <> m
> 
>    lim v->+0: normcdf(x,m,v) == 0.5     for x == m
>    lim v->+0: normcdf(x,m,v) == 1       for x  > m
>    lim v->+0: normcdf(x,m,v) == 0       for x  < m
> 
>    lim v->+0: norminv(p,m,v) ==  m      for 0 < p < 1 
>    lim v->+0: norminv(p,m,v) == -inf    for p = 0  
>    lim v->+0: norminv(p,m,v) == +inf    for p = 1  
>    lim v->+0: norminv(p,m,v) ==  nan    for p<0, p>1  
> 
> lim v->-0 is not meaningful, because the variance (and standard
> deviation) must 
> be non-negative. 
> 
> Alois 
>   


NORMPDF, NORMCDF and NORMINV are now implemented according to this.
The functions are available at octave-forge/extra/NaN.

They are compatible with Octave and Matlab. 


Alois