[SciPy-user] lognormal distribution

[Robert Kern]

Gary wrote:
> Stephen Walton wrote:
> 
>> An application question for a change:  I need to produce pseudorandom 
>> numbers drawn from a lognormal distribution (see 
>> http://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm).  
>> Does anyone have existing code for this in Numeric or numarray?
> 
> 
> It is interesting to me to see this question.
> 
> If I understand you correctly, I can say that Speakeasy has what you 
> want.  Actually, Speakeasy can produce random numbers from any 
> user-defined distribution, even one that is not analytical.    A 
> colleague of mine once (in the early '90s) used that capability in 
> modeling nuclear scintillation detectors.  He took a *measured* pulse 
> height distribution from a PMT and used it to generate random numbers 
> that he input into a model of a scintillation crystal.   His "Monte 
> Carlo" simulation was 13 lines long.
> I was intrigued by the usefulness of this feature, so I always have my 
> eye open to see if any other software package has that capability.   I 
> haven't searched exhaustively, but I haven't seen it in Matlab (or 
> octave or scilab) or Mathematica or Mathcad.   Or any of the usual 
> python packages.

Well, it depends on how tricky the function is.

If it's univariate, and you can write out the pdf or cdf as a function, 
then I believe you can subclass scipy.stats.rv_continuous, and it's 
rvs() method will numerically invert the cdf to generate it's random 
numbers.

If the function is highly multivariate, you might need to do 
Markov-Chain Monte Carlo which is implemented by PyMC.

If you have a bunch of data points from a continuous distribution, but 
no functional description, then you can make a kernel density estimate 
and draw random numbers from that. As of last night, that functionality 
is in scipy.stats.gaussian_kde.

Resampling from discrete data is pretty trivial to handwrite.

Is there anything else you need?

-- 
Robert Kern
rkern at ucsd.edu

"In the fields of hell where the grass grows high
  Are the graves of dreams allowed to die."
   -- Richard Harter