Effect of sample size and number of boostrap samples

A difficult problem to address is to determine the minimum sample size and the numbers of bootstrap samples to be used for obtain sampling distribution that makes a better fit to the true sampling distribution using the bootstrap methodology. We evaluate the effect of sample size and the number of bootstrap samples in the estimates of the mean, variance and some quantiles for probability distribution under different measures of skewness. We give some recommendations for using the non-parametric bootstrap.