[math] RandomData: Zero variance in Gaussian distribution?

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[math] RandomData: Zero variance in Gaussian distribution?

Paul Doyle-3
The RandomData interface stipulates that the standard deviation value for a call to nextGaussian(double mu, double sigma) should be greater than zero.  Can anybody explain to me why this restriction exists?

I would like to use a range of standard deviation values, including at times a value of zero resulting in a return value equal to the specified mean value.  The above restriction prevents this.  I can work around this easily enough but now I'm wondering if there is a good reason not to do so.

Thanks in advance -

Paul

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[math] RandomData: Zero variance in Gaussian distribution?

Paul Doyle-3
The RandomData interface stipulates that the standard deviation value for a call to nextGaussian(double mu, double sigma) should be greater than zero.  Can anybody explain to me why this restriction exists?
 
I would like to use a range of standard deviation values, including at times a value of zero resulting in a return value equal to the specified mean value.  The above restriction prevents this.  I can work around this easily enough but now I'm wondering if there is a good reason not to do so.
 
Thanks in advance -
 
Paul


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Re: [math] RandomData: Zero variance in Gaussian distribution?

J.Pietschmann
Paul Doyle wrote:
> The RandomData interface stipulates that the standard deviation value
> for a call to nextGaussian(double mu, double sigma) should be greater
> than zero.  Can anybody explain to me why this restriction exists?

It is a restriction of the distribution itself, rather than an
implementation restriction. See
  http://mathworld.wolfram.com/GaussianFunction.html

Given that the standard deviation is in the denominator of a
subexpression in the distribution function, it seems unwise to
allow a value of zero.

J.Pietschmann

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RE: [math] RandomData: Zero variance in Gaussian distribution?

Paul Doyle-3
In reply to this post by Paul Doyle-3
That is interesting, if is a little counterintuitive; it seems reasonable to speak of sampling from a normal distribution with standard deviation approaching or equal to zero.  Yet, as you point out, this could lead to division by zero - at least using this formulation of the probability function.

Thanks for the reply and for the excellent pointer.

Paul

-----Original Message-----
From: J.Pietschmann [mailto:[hidden email]]
Sent: 08 August 2005 21:24
To: Jakarta Commons Users List
Subject: Re: [math] RandomData: Zero variance in Gaussian distribution?


Paul Doyle wrote:
> The RandomData interface stipulates that the standard deviation value
> for a call to nextGaussian(double mu, double sigma) should be greater
> than zero.  Can anybody explain to me why this restriction exists?

It is a restriction of the distribution itself, rather than an
implementation restriction. See
  http://mathworld.wolfram.com/GaussianFunction.html

Given that the standard deviation is in the denominator of a
subexpression in the distribution function, it seems unwise to
allow a value of zero.

J.Pietschmann


This e-mail and any files transmitted with it are confidential and may be privileged and are intended solely for the individual named/ for the use of the individual or entity to whom they are addressed.If you are not the intended addressee, you should not disseminate, distribute or copy this e-mail.Please notify the sender immediately if you have received this e-mail by mistake and delete this e-mail from your system.If you are not the intended recipient, you are notified that reviewing, disclosing, copying, distributing or taking any action in reliance on the contents of this e-mail is strictly prohibited.Please note that any views or opinions expressed in this e-mail are solely those of the author and do not necessarily represent those of Traventec Limited. This e-mail has been swept for computer viruses however Traventec Limited accepts no liability for any damage caused by any virus transmitted by this e-mail.