Simulation Approach Used for the Second L-Moment Derivation of the Inverse Gaussian Distribution

摘要

Maximum Likelihood (ML) estimate of upper quantiles looses its optimal properties if a wrong distribution is assumed in the ML procedure. Since its estimates base on the main probability mass, the alternative estimation techniques yielding estimates more dependent on upper tail elements of a sample are of interest in flood frequency analysis (FFA). Several systems of describing the shape of probability distribution have been developed and used for matching the assumed distribution to the data. One of them is the system basing on the linear moments. The L-moment estimates have highly desirable properties, like small bias and no algebraic bound ofL-moment estimate ratios. It is shown how to use the //-moment system for probability distribution description if the analytical formulas of the linear moments have not been derived. The inverse Gaussian distribution serves as an example.