Difference between revisions of "Weibull distribution"
m
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  [[Var..Do|Var]] Fx :=  ([[Rank]](Data,I) - 0.5) / [[Size]](I);
 
  [[Var..Do|Var]] Fx :=  ([[Rank]](Data,I) - 0.5) / [[Size]](I);
 
  [[Var..Do|Var]] Z := [[Ln]](-[[Ln]](1-Fx));
 
  [[Var..Do|Var]] Z := [[Ln]](-[[Ln]](1-Fx));
−
  [[Var..Do|Var]] fit := [[Regression]](Z,[[Array]](bm,[1,[[Ln]](x)]),I,bm);
+
  [[Var..Do|Var]] fit := [[Regression]](Z,[[Array]](bm,[1,[[Ln]](Data)]),I,bm);
 
  [[Var..Do|Var]] shape := fit[bm='m'];
 
  [[Var..Do|Var]] shape := fit[bm='m'];
 
  [[Var..Do|Var]] b := fit[bm='b'];
 
  [[Var..Do|Var]] b := fit[bm='b'];
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= See Also =
 
= See Also =
  
 +
* [[Dens_Weibull]]
 +
* [[CumWeibull]]
 
* [[Gamma]], [[Normal]]
 
* [[Gamma]], [[Normal]]

Revision as of 22:17, 5 August 2009


Weibull( shape, scale )

The Weibull distribution is often used to represent failure time in reliability models. It is similar in shape to the gamma distribution, but tends to be less skewed and tail-heavy. It is a continuous distribution over the positive real numbers.

The Weibull distribution has a cumulative density given by

Weibull cdf eq.jpg

Library

Distribution

Example

Weibull(10,4) → Weibull graph.jpg

Parameter Estimation

Suppose you have sampled historic data in Data, indexed by I, and you want to find the parameters for the best-fit Weibull distribution. The parameters can be estimated using a linear regression as follows: 

Index bm := ['b','m'];
Var Fx :=  (Rank(Data,I) - 0.5) / Size(I);
Var Z := Ln(-Ln(1-Fx));
Var fit := Regression(Z,Array(bm,[1,Ln(Data)]),I,bm);
Var shape := fit[bm='m'];
Var b := fit[bm='b'];
Var scale := Exp(-b/shape);
[shape,scale]

See Also

Comments


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