{smcl}
{* *! version 1.0.0 29jul2010}{...}
{hline}
{cmd:help paretowml}{right:Michal Brzezinski (July 2010)}
{hline}

{title:Title}

{p2colset 5 20 22 2}{...}
{p2col: {hi:paretowml} {hline 2}}Estimate the shape parameter {it:a} for 
the Pareto (Type I) distribution using weighted maximum likelihood estimator{p_end}
{p2colreset}{...}


{title:Syntax}

{p 4 4 2}
{cmd:paretowml} [{varname}] [{cmd:,}  {it:options}]


{synoptset 20 tabbed}{...}
{synopthdr}
{synoptline}
{synopt:{bf:k({it:scalar})}}the maximum number of extreme order statistics used in estimation{p_end}
{synopt:{bf:x0({it:scalar})}}the value of scale parameter for Pareto model{p_end}
{synopt:{bf:c({it:scalar})}}robustness constant{p_end}

{p 4 4 2}
If neither {it:k} nor {it:x0} options are used, {it:x0} is set to the minimum value of {it:varname}.

{title:Description}

{p 4 4 2}
{cmd:paretowml} estimates the shape parameter {it:a} for 
the Pareto (Type I) distribution using weighted maximum likelihood estimator (WMLE). As it
is well-known ML estimation of {it:a} (see {help paretofit}) 
is very sensitive to extreme observations. WMLE downweights observations, which are inconsistent 
with Pareto model in terms of the residuals with respect to the Pareto regression model. 
For details, see (Dupuis and Victoria-Feser, 2006).

{p 4 4 2}
For implementations of non-robust and robust criteria for choosing 
scale parameter{it:x0}, introduced in Dupuis and Victoria-Feser (2006), see {help nrpec} and {help rpec}, if installed. 


{title:Examples}

{pstd}To estimate {it:a} with {it:x0} = 1000:{p_end}

{phang2}{cmd:. paretowml {it:varname}, x0(1000)}{p_end}

{pstd}To estimate {it:a} using {it:x0} estimated by
applying robust Pareto error criterion of Dupuis and Victoria-Feser (2006):  {p_end}

{phang2}{cmd:. rpec {it:varname}, k(100) }{p_end}
{phang2}{cmd:. scalar x0=r(x0)}{p_end}
{phang2}{cmd:. paretowml {it:varname}, x0(x0) }{p_end}


{title:References}

{phang}
Dupuis, Debbie J. and Victoria-Feser, Maria-Pia (2006). A Robust Prediction
 Error Criterion for Pareto Modelling of Upper Tails. {it:The Canadian Journal of Statistics}, {cmd: 34} (4), 639-658.


{title:Also see}

{p 4 13 2}
Online: help for {help nrpec}, {help rpec}, {help paretofit}, {help paretoobre}, {help hillp} if installed. 


{title:Author}

{p 4 4 2}
Michal Brzezinski <mbrzezinski@wne.uw.edu.pl>, Faculty of Economic Sciences, University of Warsaw, Poland.