Given min and max values, how can I estimate shape parameter (tail index) of data generated by truncated pareto distribution ? I see a package tpareto but find no information on how to estimate tail index from given data.
kindly help.
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set.seed(1); data = rtpareto(100, 1,10,2); ll = function(par){ if(par[1]>0&par[3]>0&par[2]>par[1]) return( -sum(log(dtpareto(data,par[1],par[2],par[3]))) ) else return(Inf) }; optim(c(1,10,2),ll);. (Requires VGAM) – user10525 Aug 16 '12 at 12:52set.seed(1); data = rtpareto(100, 1,10,2); ll = function(par){ if(par>0) return( -sum(log(dtpareto(data,1,10,par))) ) else return(Inf) }; optimize(ll,c(1,3));. – user10525 Aug 16 '12 at 13:20$minimumgives you the estimator. In this case the approach used is MLE and this value is called the Maximum Likelihood Estimator. The functionllis the negative of the log-likelihood. The optimisation is conducted using the commandoptimize. Information about the algorithm implemented in this command can be found here. Theory about the estimation of the parameters of this distribution here. – user10525 Aug 16 '12 at 13:47