Using neural network to estimate weibull parameters

Abstract

As is well known, estimating parameters of the tree-parameter weibull distribution is a complicated task and sometimes contentious area with several methods vying for recognition. Weibull distribution involves in reliability studies frequently and has many applications in engineering. However estimating the parameters of Weibull distribution is crucial in classical ways. This distribution has three parameters, but for simplicity, a parameter is ridded off and as a result, the estimation of the others will be easily done. When the three-parameter distribution is of interest, the classical estimation procedures such as maximum likelihood estimation (MLE) will be quite boring. In this paper to take advantage of application of artificial neural networks (ANN) to statistics, we propose using a simple neural network to estimate three parameters of Weibull distribution simultaneously. Trained neural network similar to moment method estimates Weibull parameters based on mean, standard deviation, median, skewness and kurtosis of the sample accurately. To assess the power of the proposed method we carry out simulation study and compare the results of the proposed method with real values of the parameters.