Bootstrapping Normal and Binomial Distributions

Abstract

This paper examines and compares the implications of bootstrapping normal and binomial distributions. Hypothetical data set was used aided by S-plus package. Data analysis, examination, and comparison were based on their correlation coefficients and the bootstrap estimate of the standard error of plug-in correlation coefficient. Evidence shows that both distributions behave very well as seen in the fundamental theory of statistics. Also as the bootstrap level increases, the binomial gives a lower correlation coefficient (-0.07258132), against -0.1355295 in normal distribution. It is pertinent to note that the correlation coefficient is steady as the bootstrap increases.The paper therefore focuses on the performance of the standard error of plug-in correlation coefficient. Result shows that the normal distribution gives lower standard error which suggests more reliability to the plug-in estimate. Thus, this study uses the bootstrap method to demonstrate a scenario where the normality assumption becomes stronger as the bootstrap sample sizes (100, 500, and 1000) gets larger but on approximation at two decimal places, both distributions give the same statistical inference (1000: 0.14). Therefore, binomial distribution is preferred to normal distribution in terms of their correlation coefficient but the normal distribution is preferred to binomial for carrying out further analysis in parameter estimation and other statistical inference in terms of their standard error of plug-in correlation coefficient.