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From "Paul Doyle" <>
Subject RE: [math] RandomData: Zero variance in Gaussian distribution?
Date Tue, 09 Aug 2005 17:11:10 GMT
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.


-----Original Message-----
From: J.Pietschmann []
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

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.


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