On testing the log-gamma distribution hypothesis by bootstrap

In this paper we propose two bootstrap goodness of fit tests for the log-gamma distribution with three parameters, location, scale and shape. These tests are built using the properties of this distribution family and are based on the sample correlation coefficient which has the property of invariance with respect to location and scale transformations. Two estimators are proposed for the shape parameter and show that both are asymptotically unbiased and consistent in mean-squared error. The test size and power is estimated by simulation. The power of the two proposed tests against several alternative distributions is compared to that of the Kolmogorov-Smirnov, Anderson-Darling, and chi-square tests. Finally, an application to data from a production process of carbon fibers is presented.