CSI 779 / STAT 789
Characteristics of Probability Densities; Q-Q Plots
For most continuous random variables we can write a
probability density function (PDF),
which is yields the relative probability that the random variable takes
values in given intervals.
Three of the most important characteristics of random variables
the moments (mean, variance, etc.) and
the shape of the density (assuming it exists).
The normal distribution is the standard for comparison. The shapes of
distributions may be
bimodal (or multimodal)
The relative frequencies and the order statistics of a
random sample from a given distribution will be "similar to" those of
the parent distribution.
A histogram and a q-q plot of the sample
are useful in assessing the shape.
Skewed; Lognormal: xx<-rlnorm(500)
Heavy-Tailed; t(5): xx<-rt(500,5)
Mixture that is not bimodal: