Investigating the Least Sample Size for Convergence to Normality from Quantile Measure of Continuous Distributions with R

For testing of hypothesis, the knowledge of the distribution of the test statistic is necessary to find the cut-off point or the p-value. But in most of the cases, the distribution of quantile measures of samples is not known or not standard or complicated. Thus, for testing the value of quantile measures the common practice is to use the asymptotic distribution of the statistic which is normal in general. But for this asymptotic distribution to be accurate the sample size must be large. Now the question is how large the sample size should be to ensure the convergence of the statistic to a normal distribution. This paper proposes a procedure to find the least Sample size required for some selected continuous distributions to converge to normality using the Shapiro-Wilks Test of Normality. Simulation and Visualisation are done in the R programming language.