Estimating the Parameters of a Two-parameter Crack Distribution

Abstract

The crack distribution is the mixture of an inverse Gaussian distribution and a length-biased inverse Gaussian distribution introduced by Jorgensen et al. [1] and Bowonrattanaset et al. [2]. The probability density function of this distribution has a complicated form that is problematic in parameter estimation. Saengthong and Bodhisuwan [3] try to solve this problem by introducing the new two-parameter crack distribution but the parameter estimate still had a problem. Therefore, optimization techniques had to be used. For this reason, we offer an alternative algorithm, an EM-algorithm, to estimate two unknown parameters of a two-parameter crack distribution which is presented in Saengthong and Bodhisuwan [3]. A Monte Carlo simulation study was conducted to appraise the performance of the proposed EM-algorithm and compared with the quasi-Newton method for the given sample sizes. The results from the simulation study show that the proposed method performed very well for both parameters and provide consistent statistics, while the quasi-Newton method is a poor estimate of the parameter.