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Re: DiscreteUniformDistribution PDF isn't piecewise?

• To: mathgroup at smc.vnet.net
• Subject: [mg107700] Re: DiscreteUniformDistribution PDF isn't piecewise?
• From: Peter Falloon <pfalloon at gmail.com>
• Date: Tue, 23 Feb 2010 08:04:44 -0500 (EST)
• References: <hlqu3v$go8$1@smc.vnet.net> <201002220807.DAA28826@smc.vnet.net>

>
> The problem with a PMF is one we've already seen: 1/6& isn't a PMF (or PDF)
> at all, unless we know its accompanying domain. It could be uniform discrete
> on ANY 6 numbers or other objects.
>

I agree; what I'm trying to say is that a possible solution for a PMF (as
opposed to a PDF) is as you suggested, except replacing DiracDelta by
KroneckerDelta:

    myPDF[DiscreteUniformDistribution[{imin_Integer,imax_Integer}], x_] :=

        (1/(imax-imin+1))*Sum[KroneckerDelta[x,i], {i,imin,imax}]

This has the desired behaviour for a PMF (which, according to the
documention, is what the Mathematica implementation seeks to provide for
discrete distributions such as this one) -- whereas the DiracDelta version
would be appropriate for a PDF.

Cheers,
Peter.

• References:
  • Re: DiscreteUniformDistribution PDF isn't piecewise?
    • From: "Nasser M. Abbasi" <nma@12000.org>