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Re: WeibullDistribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg42449] Re: WeibullDistribution
  • From: bobhanlon at aol.com (Bob Hanlon)
  • Date: Wed, 9 Jul 2003 08:24:25 -0400 (EDT)
  • References: <bee0f9$fhd$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Needs["Statistics`ContinuousDistributions`"];

data=RandomArray[WeibullDistribution[5, 2],{100}];

To get an initial estimate of the parameters

est = FindRoot[{
      Mean[WeibullDistribution[a, b]]==Mean[data],
      Variance[WeibullDistribution[a, b]]==Variance[data]}, 
    {a,1},{b,1}]

{a -> 4.882178679882784, b -> 1.9493985547665071}

You want to maximize the log likelihood function given by

llf = Simplify[Plus @@ (Log[PDF[WeibullDistribution[a,b],#]]& /@ data)];

The MLE estimates of the parameters are then

FindRoot[Evaluate[{D[llf,a]==0,D[llf,b]==0}],
  {a,est[[1,2]]}, {b, est[[2,2]]}]

{a -> 4.923904837274986, b -> 1.9483453144994602}


Bob Hanlon

In article <bee0f9$fhd$1 at smc.vnet.net>, ce.choa.phen.kee at philips.com wrote:

<< I have a set of data, but how can I find out the A and B in 
WeibullDistribution[ A , B ] ?

There isn't much informaion regarding the WeibullDistribution provided in 
the Help Browser. Anyone pls help???


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