Log-Logistic model



   [loglogistic_ex1]
   
   model
   {
      for( i in 1 : N )
      {
            x[i] ~ dlog.logis(beta, theta)
      }
      
   # Prior distributions of the model parameters    
   
         beta ~ dunif(0.1, 10.0)
         theta~ dunif(0.1, 10.0)   
   }

The 40 observations are generated from Log-logistic distribution with beta=3.0 and theta = 5.0

The MLEs are beta.mle= 2.97937, theta.mle= 4.82757

Data
list(N=40, x=c(0.92, 1.24, 1.64, 2.03, 2.43, 2.44, 3.26, 3.32, 3.41, 3.42, 3.44, 3.54,
3.60, 3.71, 3.82, 3.94, 4.05, 4.17, 4.20, 4.69, 4.69, 4.81, 5.11, 5.43, 5.99, 6.23, 6.39, 6.44, 6.80, 7.49, 7.65, 7.96, 8.25, 9.00, 9.08, 9.48, 10.42, 11.79, 11.96, 12.03))
Inits for chain 1
list(beta=1.5, theta=4.0)
   
Inits for chain 2
list(beta=6.5, theta=6.0)



Results

[loglogistic_ex2]

MAP estimates are

[loglogistic_ex3]

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