Help me find a probability distribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg114614] Help me find a probability distribution*From*: mathlawguy <chandler.seth at gmail.com>*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.