The Q-Q estimator and heavy tails.

Marie Kratz (1) , Sid Resnick (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 ORIE - School of Operations Research and Information Engineering

A common visual technique for assessing goodness of fit and estimating location and scale is the qq--plot. We apply this technique to data from a Pareto distribution and more generally to data generated by a distribution with a heavy tail. A procedure for assessing the presence of heavy tails and for estimating the parameter of regular variation is discussed which can supplement other standard techniques such as the Hill plot. Some examples are given using telecommunications data.

Mots clés: parameter estimation; weak convergence; consistency; time series analysis; qq-plot; heavy tails; regular variation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Marie Kratz, Sid Resnick. The Q-Q estimator and heavy tails.. Stochastic Models, 1996, 12 (4), pp.699-724. ⟨10.1080/15326349608807407⟩. ⟨hal-00179391⟩