| Re: Normal Distributed Random Numbers [message #26517] |
Tue, 04 September 2001 14:34 |
thompson
Messages: 584
Registered: August 1991
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Senior Member |
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"Kay Bente" <KBente@lycos.de> writes:
> Hi
> I have to create arrays with normal distributed random numbers, but with
> variable FWHM (Full width half max/standard deviation sigma?).
> I want to add normal distributed noise to an image, so that the values
> differ around a mean value.
> In IDL there is a procedure to create such arrays RandomN, but you can't
> change the FWHM and I can't find what FWHM the normal distribution there
> has.
> So I would be glad If somone can tell me how to create such arrays (maybe
> outof uniform distributed arrays created with RandomU, I have no idea.
> I'm using IDL 5.4
The RANDOMN() function creates a Gaussian distribution with an average of 0,
and a standard deviation of 1. Mathematically, this is written as
EXP(-0.5*X^2)
If you want a different distribution, e.g. a different average or a different
standard deviation, all you need to do is something
RanVals = AvgVal + Sigma*RANDOMN(Seed, Num)
For example,
RanVals = 500 + 3*RANDOMN(Seed, 10000)
would produce a bunch of random numbers with an average value of 500, and a
standard deviation of 3. In other words, most of the numbers would be between
497 and 503.
(The FWHM of this distribution is 2*Sigma*SQRT(2*ALOG(2)), or about 2.35*Sigma,
but I suspect you're really thinking about the standard deviation Sigma rather
than the FWHM.)
William Thompson
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| Re: Normal Distributed Random Numbers [message #26518 is a reply to message #26517] |
Tue, 04 September 2001 14:24  |
James Kuyper
Messages: 425
Registered: March 2000
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Senior Member |
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Kay Bente wrote:
>
> Hi
> I have to create arrays with normal distributed random numbers, but with
> variable FWHM (Full width half max/standard deviation sigma?).
> I want to add normal distributed noise to an image, so that the values
> differ around a mean value.
> In IDL there is a procedure to create such arrays RandomN, but you can�t
> change the FWHM and I can�t find what FWHM the normal distribution there
> has.
For a normal distribution, FWHM = 2*sqrt(alog(2))*(standard deviation)
RandomN produces a distribution with a mean of 0 and a standard
deviation of 1.0. Therefore, to create an array with a desired mean
value and a desired value for FWHM, use:
array = mean + fwhm*RandomN(Seed, N)/(2*sqrt(alog(2)))
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| Re: Normal Distributed Random Numbers [message #26519 is a reply to message #26518] |
Tue, 04 September 2001 14:04 |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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"Kay Bente" <KBente@lycos.de> writes:
> Hi
> I have to create arrays with normal distributed random numbers, but with
> variable FWHM (Full width half max/standard deviation sigma?).
> I want to add normal distributed noise to an image, so that the values
> differ around a mean value.
> In IDL there is a procedure to create such arrays RandomN, but you can�t
> change the FWHM and I can�t find what FWHM the normal distribution there
> has.
From the IDL Reference Guide:
> The RANDOMN function returns one or more normally-distributed,
> floating-point, pseudo-random numbers with a mean of zero and a
> standard deviation of one.
So there you go, the deviates produced by RANDOMN have a gaussian
sigma of 1, like this:
S = RANDOMN(SEED, 1000)
And then it's well established for a gaussian distribution that if you
want a new mean, MU, and new gaussian sigma, SIG, then you would apply
the following formula:
SPRIME = S*SIG + MU
And, knowing that gaussian sigma is approximately SIG = FWHM / 2.35,
you are set. The key here is that SIG can be an array, not just a
scalar, so you can have a different value of SIG (and hence FWHM) for
each pixel.
Good luck,
Craig
--
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Craig B. Markwardt, Ph.D. EMAIL: craigmnet@cow.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
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