The estimation of the self-similarity parameter in linear fractional &agr;-stable motion (0<&agr;<2) is addressed in this paper.

Leland et al. have shown that typical traces of ethernet traffic are approximately statistically self-similar with parameter greater than 1/2. The authors introduce two estimation procedures, based on a wavelet transform and a finite impulse response transformation (FIRT). The power and logarithmic estimators are introduced, and their asymptotical statistical properties are derived. Simulations comparing the estimators are given.

The FIRT estimator was shown to perform better than the wavelet transform for 0<&agr;<1. For &agr;>1, both perform well. The authors suggest more extensive simulations with a variety of wavelet transforms.