Hi,
   
  I have some problems – I have a Cauchy distribution with density function 
   
  f(x) = sigma / (pi * (sigma^2 + (x- miu)^2) ), 
   
  where sigma = scale and miu = location (in my case sigma = 3, miu = 0), and I have to find with bootstrap
   
  E | sigma_estimated^3 – sigma^3 |  (#),
   
  where sigma_estimated, I guess, is  bootstrap estimate. 
   
  So, I can find sigma with R function fitdistr() from the real data, witch are generated with rcauchy(1000, 0, 3), I guess sigma_estimated I can find with  function fitdistr too, but I don’t know how to take just scale column. Anyone knows? 
   
  Ok, if my bootstrap will have R=1000 I have to find (#) something like this:
   
  E | sigma_estimated^3 – sigma^3 | = (1/R) * sum (r = 1:R) [|sigma_boot(r)^3 – sigma^3|]?
   
  Next problem – I have with kernel estimate a density f() function? How can I do this with R?
   
  And the last – with bootstrap I have to estimate a characteristic function, witch is 
   
  c = exp{i*t*miu – sigma|t|} (in my case it will be c = exp{– sigma|t|})? Is it possible to solve this problem with R?
   
   
   
  Sorry for my broken English and huge thanks to everyone who will help me! :)
   

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