Generalized Exponential model

   
   
   model
   {
      for( i in 1 : N )
      {
      x[i] ~ dgen.exp(alpha, lambda)
      }
      
   # Prior distributions of the model parameters   
         alpha~ dgamma(0.001, 0.001)
         lambda~ dgamma(0.001, 0.001)   
   }

The data given here arose in tests on endurance of deep groove ball bearings.The data are the number of million revolutions before failure for each of the 23 ball bearings in the life test. The data are taken from Lawless (2003, pp. 99).

Lawless, J.F. (2003). Statistical Models and Methods for Lifetime data, Second edition, John Wiley & Sons, New York.

The MLE’s are  alpha = 5.2589; lambda = 0 .0314

   


list(alpha = 5.2589; lambda = 0 .0314)

list(alpha = 5.28348, lambda = 0.0322971)

Results

Using a slightly modified model

model
   {
      for( i in 1 : N )
      {
      x[i] ~ dgen.exp(alpha, lambda)
      }
      
   # Prior distributions of the model parameters   
         alpha~ dunif(0, 25)
         lambda~ dunif(0, 0.25)
         diffAlpha <- diffLC(alpha)
         diffLambda <- diffLC(lambda)
   }
   
Compile 10 chains, monitor alpha, lambda and deviance. Using last iteration to get reults of
alpha = 5.28348, lambda = 0.0322971 and deviance = 225.952.