[SciPy-user] lognormal distribution

[Gary]

Robert Kern wrote:

> 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?
>
World peace and/or longer prison sentences for parole violators?       

I wasn't aware of  the rvs() method.  Now I am.
I've never heard of kernel density estimate.  Now I have.  I think I'll 
try it out on data from the intro physics lab that I teach.  The 
students are seeing histograms for the first time, and they don't like 
it when the ones they get with their data don't look like the nice bell 
curves in the book.

Thanks,
gary