Kernel density estimation of three-parameter Weibull distribution with neural network and genetic algorithm

- The initial estimations were obtained by the RRM and GM(1, 1).
- The proposed way to deal with the estimation problem was an optimization problem.
- Neural network was adopted as approximate model based on the samples.
- GA was selected for optimization method based on the neural network model.

Three-parameter Weibull distribution is widely employed as a model in reliability and lifetime studies due to its good fit to data. It is important to estimate the unknown parameters exactly for modeling. There are many methods to estimate the parameters of three-parameter Weibull distribution and the kernel density estimation method is one of them. The smoothing parameter has a significant influence on the estimation accuracy. In this paper, the neural network and genetic algorithm were used to get the best smoothing parameter and the result was compared with other methods. The Monte Carlo simulations were carried out to show the feasibility of our approach for estimation of three-parameter Weibull distribution.