Fitting concentration data with stable distributions
Over the last several years there has been a growing interest in applying stable distribution to model real data. The lack of closed formulas for densities and distribution functions for all but few stable distributions has been a major drawback to the use of stable distributions by practitioners. There are now reliable computer programs to compute stable densities, distribution functions and quantiles. In this work, we try to model concentration data with stable distributions. We developed several computer programs to estimate the stable distribution parameters given concentration data in one and two dimensions. Confidence intervals are derived using bootstrap and profile likelihood approaches in the univariate case. Simulations are used to test and compare these methods and then apply them to real concentration data.