Parameter estimation of Gumbel distribution and its application to pitting corrosion depth of concrete girder bridges

Taking pitting corrosion depth uncertainty into account is key to approach durability analysis of concrete girder bridges in a probabilistic way. The Gumbel distribution has been widely used to represent the probability distribution of pitting corrosion depth. In this study, Bayesian Quantile method was used to estimate the parameters of the Gumbel distribution. The proposed method was also compared with the commonly used maximum likelihood method via an extensive numerical simulation and two real pitting corrosion depth data examples based on performance measures such as, K–S test, RMSE, and R2. The numerical study reveals that the Bayesian Quantile method is suitable for estimating the parameters of the Gumbel distribution. Statistical analysis of real pitting corrosion depth data sets are presented to demonstrate the applicability and the conclusion of the simulation results.