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st: Pareto v. lognormal


From   "Patrick Wöhrle Guimarães" <probabilidade@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Pareto v. lognormal
Date   Fri, 9 Mar 2007 20:39:26 -0300

 Looking the suggestions about fit Pareto distribution (or power law)
- i have some doubts - my desire is fit only de upper tail with de
Pareto Distribution (all the data dont good fit for Pareto
Distribution but only the upper tail - i have almost 400.000 value per
year). In general, many papers fitting income distribution use
lognormal (to fit 99% of income) and power law (to fit 1% of income) -
one question: how to set up one cutt-of (or the income level below
which the Pareto distribution would not apply)?
 It´s possible to use kdens with stratum and psu (with complex
design)? Stas talked that regularity conditions are not satisfied for
k - the variance isnt finite (the question is The Fisher information)?
 When i wrote the question my desire is estimate power law using the
more simple way: ln(1-F) = -a ln x + a ln k. My problems was with
large dateset establish a cutt-of to fit Pareto Distribution only for
the upper tail. Other problem was that Im working with complex design
(weight, stratum and psu) and for me the best estimator to use with
complex design was pseudo-log-likelihood.
Kdens, quantile plot, ...I dont have good idea which is the best way
to estimate Pareto distribution using all information in complex
design with a logical (or clear) cutt-off but the suggestions is very
good. Thanks all!

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