Birnbaum-Saunders model



   [bs_ex1]
   
   
   model
   {
      for( i in 1 : N )
      {      
            x[i] ~ dbs(alpha, beta)
      }
      
   # Prior distributions of the model parameters   
         alpha ~ dunif(0.01, 5.0)
         beta~ dunif(0.01, 300.0)      
   }

The following data 'psi31' are taken from Birnbaum and Saunders (1969).

Birnbaum, Z. W. and Saunders, S. C. (1969). Estimation for a family of life distributions with applications to fatigue. J. Appl. Probab. 6(2), 328-347.

Leiva, V., Hernández, H., and Riquelme, M. (2006). A New Package for the Birnbaum-Saunders Distribution. Rnews, 6/4, 35-40.

The MLE's are obtained using 'bs' package in R    alpha.mle = 0.1703847 beta.mle = 131.8188

Data
list(N=101, x=c( 70, 90, 96, 97, 99, 100, 103, 104, 104, 105, 107, 108, 108, 108, 109, 109,
112, 112, 113, 114, 114, 114, 116, 119, 120, 120, 120, 121, 121, 123, 124, 124, 124, 124, 124,
128, 128, 129, 129, 130, 130, 130, 131, 131, 131, 131, 131, 132, 132, 132, 133, 134, 134, 134,
134, 134, 136, 136, 137, 138, 138, 138, 139, 139, 141, 141, 142, 142, 142, 142, 142, 142, 144,
144, 145, 146, 148, 148, 149, 151, 151, 152, 155, 156, 157, 157, 157, 157, 158, 159, 162, 163,
163, 164, 166, 166, 168, 170, 174, 196, 212))
Inits for chain 1
list(alpha=1.0, beta=50.0)
   
Inits for chain 2
list(alpha=2.0, beta=200.0)



Results

[bs_ex2]
MAP estimates are
[bs_ex3]

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