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Luis A. Afonso
Posts:
4,758
From:
LIsbon (Portugal)
Registered:
2/16/05


An overwhelming statement Reporting to a Re: How to simulate Cauchy sa
Posted:
Oct 1, 2013 1:37 PM


An overwhelming statement
Reporting to a Re: How to simulate Cauchy samples Posted: May 8, 2008 7:54 AM From Jack Tomsky: _____These are not confidence intervals on the median. Since you're assuming that the population median is known to be zero, the confidence interval for the median is [0, 0] for all confidence levels. Jack (moderator) ___________ I think that this statement should be fully discussed by two main reasons: ___1) It could be understood as the simulation Monte Carlo is wrong/unuseful/dangerous. ___2) The sampling of simulated data *losses/harms* its mainly valuable property of to be random.
___1) A not really strong argument is that Monte Carlo in Statistics/ NHST is used since early sixties, any contest was appeared. Remember that an early paper on the issue is authorized by Hubert Lilliefors who adapted Kolmogorov Smirnov normal test to the case where the parameters are unknown, so estimated by data itself. ___2) About randomness. Given the (Cumulative) Distribution Function of the r.v. X, F(X<=x0) = g(x0; a,b, ...), a, b, ... parameters, we can invert then to obtain the result: Prob. (x0<= a) = G(F(a)) where G is the inverse function of the CDF. Now let be F= random on [0,1], then we have Prob.(x0<= a) = G(random). Given a random number u and evaluating G(u) we get easily the value x0 which is *at random*, exactly and unquestionably. Jack Tomsky´s argument that because I let the median as zero the C.I, is [0, 0] is completely worthless. I am full free to chose the parameter´s values at my criterion, to pick what model I want to work with.
Luis A. Afonso



