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Re: Help me find a probability distribution
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.