Another of my papers on analytic bias-correction has now been published. This one is with a former M.A. student, Xiao Ling.
The details are: Xiao Ling and David E. Giles, "Bias reduction for the maximum likelihood estimator of the parameters of the generalized Rayleigh family of distributions. Communications in Statistics - Theory and Methods, 2014, 43, 1778-1792.
You can see the paper here.