Date: Feb 7, 2013 2:21 PM
Author: Luis A. Afonso
Subject: Sample Distributions by Simulation

Sample Distributions by Simulation

We are concerned with Simulated Populations.
Anteceding whatever we should define the data scheme we will work with. Essentially, exact procedure, we get, repeating M times, a unit source made of one sample, two, or more, obtained randomly by their Distribution Functions (PDF, see Note) , and its R replications, formed through a given procedure: Bootstrap, Jacknife, Permutations, or any other.
If we are dealing with the pure Source Distribution we set obviously R=0: all units are rigorously synthetically exact (if so). Ordinarily we fix the sample sizes which are the parameter more directly accessible to account in practice. This means that the study of Sample Distribution Statistics is our aim and if source is obtained by PDF and no replications are performed the proprieties issued from it are exact, but not general, of course, because we are dealing with numeric construed data. On the other hand all replication procedure are approximate at the sense that it is unable to free completely from its source features; consequently a replicate data is not accurately identical to a source one.
Note: it is not necessary (contrarily I read on Web) that one must have an invertible PDF in order to get r.v. values: numerical inversion is enough to perform the job: the procedure being exact in the sense that one can obtain as decimal places as we need.

Luis A. Afonso