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John O'Neill  
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 More options Oct 24 2012, 5:38 pm
Newsgroups: comp.lang.idl-pvwave
From: "John O'Neill" <j1701j...@gmail.com>
Date: Wed, 24 Oct 2012 14:38:34 -0700 (PDT)
Local: Wed, Oct 24 2012 5:38 pm
Subject: Random Numbers
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Hello Everyone,

I am trying to create a set of random numbers using an Inverse Gaussian Distribution (Wald distribution) but randomu doesn't seem able to do this.  Is there anything more general then randomu, or something where I can define what function I want to use to create random numbers?

Thanks.


 
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Craig Markwardt  
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 More options Oct 24 2012, 7:34 pm
Newsgroups: comp.lang.idl-pvwave
From: Craig Markwardt <craig.markwa...@gmail.com>
Date: Wed, 24 Oct 2012 16:34:39 -0700 (PDT)
Local: Wed, Oct 24 2012 7:34 pm
Subject: Re: Random Numbers
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On Wednesday, October 24, 2012 5:38:34 PM UTC-4, John O'Neill wrote:
> Hello Everyone,

> I am trying to create a set of random numbers using an Inverse Gaussian Distribution (Wald distribution) but randomu doesn't seem able to do this.  Is there anything more general then randomu, or something where I can define what function I want to use to create random numbers?

http://en.wikipedia.org/wiki/Inverse_transform_sampling

I'm not aware of any IDL routines to do this though, but it's not hard with a little integrating and interpolating.

The difficulty of implementing the method depends on the distribution to some degree.  For example, power law distributions can be hard to do because of the dynamic range required.

Craig


 
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Yngvar Larsen  
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 More options Oct 25 2012, 3:14 am
Newsgroups: comp.lang.idl-pvwave
From: Yngvar Larsen <larsen.yng...@gmail.com>
Date: Thu, 25 Oct 2012 00:14:15 -0700 (PDT)
Local: Thurs, Oct 25 2012 3:14 am
Subject: Re: Random Numbers
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On Wednesday, 24 October 2012 23:38:34 UTC+2, John O'Neill  wrote:
> Hello Everyone,

> I am trying to create a set of random numbers using an Inverse Gaussian Distribution (Wald distribution) but randomu doesn't seem able to do this.  Is there anything more general then randomu, or something where I can define what function I want to use to create random numbers?

Google and Wikipedia are your friends.

http://en.wikipedia.org/wiki/Inverse_Gaussian_distribution#Generating...

IDL> N = 100
IDL> mu = 1d0 & lambda = 1d0
IDL> nu = randomn(seed, N)
IDL> z = randomu(seed, N)
IDL> igvariates = dblarr(N)
IDL> y = nu^2
IDL> x = mu + mu^2*y/(2*lambda) - mu/2/lambda*sqrt(4*mu*lambda*y + mu^2*y^2)
IDL> ind = where(z le mu/(mu+x), complement=cind)                          
IDL> igvariates[ind] = x[ind]
IDL> igvariates[cind] = mu^2/x[cind]

Include checking for empty index arrays IND and/or CIND if you use IDL version < 8.0.

--
Yngvar


 
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David  
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 More options Oct 25 2012, 10:37 am
Newsgroups: comp.lang.idl-pvwave
From: David <n...@idlcoyote.com>
Date: Thu, 25 Oct 2012 08:37:59 -0600
Local: Thurs, Oct 25 2012 10:37 am
Subject: Re: Random Numbers
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This code is easy enough to implement that I just wrote
a function, cgRandomWald to do it this morning. You can
find it here:

   http://www.idlcoyote.com/programs/cgrandomwald.pro

It works very much like the other RandomX functions in IDL.

Cheers,

David

--
David Fanning, Ph.D.
Fanning Software Consulting, Inc.
Coyote's Guide to IDL Programming: http://www.dfanning.com/
Sepore ma de ni thue. ("Perhaps thos speakest truth.")


 
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John O'Neill  
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 More options Oct 25 2012, 11:06 am
Newsgroups: comp.lang.idl-pvwave
From: "John O'Neill" <j1701j...@gmail.com>
Date: Thu, 25 Oct 2012 08:06:46 -0700 (PDT)
Local: Thurs, Oct 25 2012 11:06 am
Subject: Re: Random Numbers
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Thank you very much David, Yngvar, and Craig for your help.  This is exactly what I was looking for.

John


 
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