Re: DiscreteUniformDistribution PDF isn't piecewise?
- To: mathgroup at smc.vnet.net
- Subject: [mg107697] Re: DiscreteUniformDistribution PDF isn't piecewise?
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Tue, 23 Feb 2010 08:04:12 -0500 (EST)
- References: <hlqu3v$go8$1@smc.vnet.net> <201002220807.DAA28826@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
I meant what I wrote, I think, except that I forgot to normalize: pdf2[x_] = Sum[DiracDelta[x - n], {n, 1, 6}]/6 1/6 (DiracDelta[-6 + x] + DiracDelta[-5 + x] + DiracDelta[-4 + x] + DiracDelta[-3 + x] + DiracDelta[-2 + x] + DiracDelta[-1 + x]) The total integral is one: Integrate[pdf2@x, {x, 0, 7}] 1 And the plotted CDF is correct: Plot[Integrate[pdf2@x, {x, 0, y}], {y, 0, 7}] That doesn't work for KroneckerDelta or DiscreteDelta. However... Table[pdf2@x, {x, 1, 6}] {DiracDelta[0]/6, DiracDelta[0]/6, DiracDelta[0]/6, DiracDelta[0]/6, DiracDelta[0]/6, DiracDelta[0]/6} So I take your point. pdf2 is a great precursor to the CDF, but a poor PDF. Bobby On Mon, 22 Feb 2010 18:13:21 -0600, gekko <pfalloon at gmail.com> wrote: > On Feb 23, 11:04 am, DrMajorBob <btre... at austin.rr.com> wrote: >> A more correct pdf for the example is >> >> Function[x, If[MemberQ[Range[1, 6], x], 1/6, 0]] >> >> An even better answer (if I'm not getting things backward) might be >> >> pdf2[x_] = Sum[DiracDelta[x - n], {n, 1, 6}] > > Of course you mean KroneckerDelta (or DiscreteDelta) rather than > DiracDelta... ;-) > > Cheers, > Peter. -- DrMajorBob at yahoo.com
- References:
- Re: DiscreteUniformDistribution PDF isn't piecewise?
- From: "Nasser M. Abbasi" <nma@12000.org>
- Re: DiscreteUniformDistribution PDF isn't piecewise?