[SciPy-User] [OT] Transform (i.e., Fourier, Laplace, etc.) methods in Prob. & Stats.

[S. Chris Colbert]

i dont know if it will be of any use to you, but:

Laplace transforms and their inversions are also used extensively in control 
theory. 

I wrote some python for the numerical inversion awhile back (before i was any 
good in python, be warned!) 

There are two different inversion methods in the attached file: the method of 
riemann sums is the faster of the two, and here is the reference from which I 
made my implementation:

http://books.google.com/books?id=CmX1aHur7jcC&pg=PA410&lpg=PA410&dq=%27%27%27This+algorithm+is+proposed+by+Tzou,
+Ozisik+and+Chiffelle+%281994%29%27%27%27&source=bl&ots=NSiw3tKRvG&sig=cqfa_ka_baPbcnhoSA9Gcxo8Vj8&hl=en&ei=YgQPS-3dKJ2qmwPO6LncBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAgQ6AEwAA#v=onepage&q=%27%27%27This%20algorithm%20is%20proposed%20by%20Tzou%2C%20Ozisik%20and%20Chiffelle%20%281994%29%27%27%27&f=false

You can probably throw out the stehfest method. I was using it originally as 
it was faster, but then I managed to vectorize the riemann method. I had no 
luck vectorizing the stehfest method. 

Cheers, 

Chris

> Sounds good, thanks again!
> 
> DG
> 
> On Thu, Nov 26, 2009 at 12:34 PM, nicky van foreest 
<vanforeest at gmail.com>wrote:
> > > Chung, K. L., 2000. "A Course In Probability Theory, 2nd Ed." Academic.
> > > looks like a really good general reference, Nicky - I assume this is
> > > the "Chung" to which you were referring?  Thanks!!!
> >
> > That is the one indeed.
> >
> > For z transforms you might like generatingfunctionoly (or something
> > like this). Search on Herbert Wilf, On his website you can find a very
> > nice book on the uses of z transforms. The first chapter is very
> > accessible.
> >
> > HOpe this helps.
> >
> > NIcky
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> 
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