 Considering the centered sample mean in this case, the random sample original distribution function formula_20 is replaced by a bootstrap random sample with function formula_21, and the probability distribution of formula_22 is approximated by that of formula_23, where formula_24, which is the expectation corresponding to formula_21.The use of a parametric model at the sampling stage of the bootstrap methodology leads to procedures which are different from those obtained by applying basic statistical theory to inference for the same model.Often the parametric bootstrap approximation is better than the empirical bootstrap approximation.