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.htmlGiven 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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