Matlab routines to estimate the tail index alpha

The generalized Central Limit Theorem has that the sum of independent, identically and symmetrically distributed random variables converges to a distribution whose tail is Pareto, with 0 < alpha <= 2. If alpha = 2, the variance is finite and the specific Central Limit Theorem applies so that the tail is Normal.

TailHill.m is a function that returns the maximum likelihood, best linear unbiased, least squares and moment estimators of the tail-index for the k largest observations.

TailWHill.m does the same, but for weighted data.

TailZipf.m is a function that returns estimators based on the QQ-plots of the k largest observations. The advantage of these estimators is that they are robust to deviations from the Pareto distribution. They should be more reliable in small samples.

TailWZipf.m does the same, but for weighted data.

TailHuisman.m is a function that returns the Huisman estimator, which is independent of tail sample size k, but requires a series of tail-index estimates as input.

ComputeTailIndices.m is a wrapper to run the scripts and draw graphs. TailIndices.m is a script to read data and write estimates.