Logistic-Exponential model



   [logisticexponential_ex1]
   
   


The data set 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).

The MLE’s are alpha = 2.366 ; lambda = 0 .01059

Lan, Y. and Leemis, L. M. (2008). The Log-Exponential Distribution. Naval Research Logistics, 55, 252-264.

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

model
   {
      for( i in 1 : N )
      {
      x[i] ~ dlogistic.exp(alpha, lambda)
      }
      
   # Prior distributions of the model parameters   
   
         alpha ~ dunif(0.0, 10)
         lambda~ dunif(0,1.0)   
   }

Data
list( N=23, x = c(17.88, 28.92, 33.00, 41.52, 42.12, 45.60, 48.80, 51.84, 51.96, 54.12, 55.56, 67.80, 68.64, 68.88, 84.12, 93.12, 98.64, 105.12, 105.84, 127.92, 128.04, 173.40, 68.64))
Inits for chain 1
list(alpha=5.0, lambda=0.5)
   
Inits for chain 2
list(alpha=3.0, lambda=0.1)



Results

[logisticexponential_ex2]

MAP estimates are

[logisticexponential_ex3]

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