# Truncated Pareto estimation

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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Check the following simulated example: 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 12:52
thanks...any suggestion how can i estimate tail index if i dont know the actual tail index of generated data ? –  asadarfeen Aug 16 '12 at 13:07
Sorry, I posted the code for obtaining the joint estimators. Given min and max, you can estimate the shape parameter using this code set.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
thanks a lot. should i interpret $minimum as value of tail index ? any reference/doc will be appreciated as I have no experience of optimization stuff which has been used above...thanks again – asadarfeen Aug 16 '12 at 13:34 Yes, $minimum gives you the estimator. In this case the approach used is MLE and this value is called the Maximum Likelihood Estimator. The function ll is the negative of the log-likelihood. The optimisation is conducted using the command optimize. 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