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Re: Help me find a probability distribution

• To: mathgroup at smc.vnet.net
• Subject: [mg114642] Re: Help me find a probability distribution
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Sat, 11 Dec 2010 01:54:52 -0500 (EST)

On 12/10/10 at 2:30 AM, chandler.seth at gmail.com (mathlawguy) wrote:

>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

A Weibull distribution with shape parameter less than or equal
to 1 will satisfy the requirements above.

That is, a WeibullDistribution[a,b] is continuous, has domain
[0, Infinity]. A constant times the hazard function of a Weibull
distribution is the hazard function of another Weibull
distribution. (In life testing, this is referred to as a
proportional hazard model). And finally for a<1 the cumulative
hazard function is decreasing, a = 1 the cumulative hazard is
constant and for a>1 the cumulative hazard is increasing.