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R's Normal Distribution Functions: rnorm and palsSubmitted by dylan on Wed, 20100714 17:10.
The rnorm() function in R is a convenient way to simulate values from the normal distribution, characterized by a given mean and standard deviation. I hadn't previously used the associated commands dnorm() (normal density function), pnorm() (cumulative distribution function), and qnorm() (quantile function) before so I made a simple demo. The *norm functions generate results based on a wellbehaved normal distribution, while the corresponding functions density(), ecdf(), and quantile() compute empirical values. The following example could be extended to graphically describe departures from normality (or some other distribution see rt(), runif(), rcauchy() etc.) in a data set. # sample a normal distribution, with a mean of 5 and sd of 2, 100 times x < rnorm(100, mean=5, sd=2) # sort in ascending order x.sorted < sort(x) # compute the empirical cumulative distribution function x.ecdf < ecdf(x.sorted) # plot the expected and actual probability density plot(x.sorted, dnorm(x.sorted, mean=5, sd=2), type='l', ylim=c(0,1), ylab='Probability', xlab='Value', main='rnorm(), dnorm(), pnorm(), and qnorm()') lines(density(x), col=1, lty=2) # add the expected and actual cumulative probability lines(x.sorted, pnorm(x.sorted, mean=5, sd=2), type='l', col=2) lines(x.sorted, x.ecdf(x.sorted), type='l', col=2, lty=2) # add the expected and actual p=0.5 (median) and p=0.95 quantiles abline(v=qnorm(c(0.5, 0.95), mean=5, sd=2), col=3) abline(v=quantile(x, probs=c(0.5, 0.95)), col=3, lty=2) # add the original x values rug(x) # annotate legend('topleft', legend=c('Probability Density','Cumulative Probability','[0.5, 0.95] Quantiles'), lty=1, col=1:3, bty='n') ( categories: )

QQ plots
The human eye is not great at differentiating curves. Any two vaguely bellshaped curves look pretty similar. A better approach to visually checking normality of sample data is using a qq plot, which is easily done in R. Try the following with your example:
qqnorm(x)
qqline(x)
QQ Plots
Thanks for the tip Sean. I agree, QQ plots are a much better approach for comparing distributions. This post was mostly about comparing those functions responsible for generating theoretical vs. estimated parameters.