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Help me find a probability distribution

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  • Subject: [mg114614] Help me find a probability distribution
  • From: mathlawguy <chandler.seth at>
  • Date: Fri, 10 Dec 2010 02:30:41 -0500 (EST)

I'm looking for a probability distribution (contained within
Mathematica 8) that has the following properties

1) continuous
2) domain is positive (or non-negative) reals
3) if one multiplies its HazardFunction by a constant, one still has a
distribution of the same class or at least a distribution that
Mathematica "knows about"
4) its HazardFunction can be decreasing or at least non-increasing for
some set of its parameters

More importantly, has anyone discovered any tricks for considering
item (3).  By way of example, suppose one wants to see if, when you
multiply the hazard function of a GammaDistribution by a constant q,
you still have a gamma distribution.   So, we ask Mathematica to
execute: DSolve[{f[0] == 1, D[f[t], t]/f[t] == q
HazardFunction[GammaDistribution[a, b], t]},
 f[t], t] and Mathematica dutifully spits back {{f[t] ->
Piecewise[{{1, t <= 0}}, Gamma[a, 0]^q/Gamma[a, t/b]^q]}}.  Cool.
But, this doesn't look like the SurvivalFunction of a
GammaDistribution or any other distribution contained in Mathematica
8.  But I'm not 100% sure.  Anyone have advice on how to make progress
tackling this problem within Mathematica.

Hope I'm being clear.

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