ABSTRACT
Continuous probability distributions are defined in terms of the probability density function and the cumulative distribution function, which are considered as population analogues of the histogram and cumulative frequency polygon. The uniform distribution is then introduced, followed by the exponential distribution. The Markov property of the exponential distribution and its genesis as the distribution of the times between events in a Poisson process. are emphasized. The normal distribution is covered and its derivation as a limit of a binomial distribution is mentioned – a proof is given on the website. Graphical methods for an informal assessment of goodness of fit using quantile-quantile plots, or equivalent probability plots is introduced. Lognormal and gamma distributions follow from the normal and exponential distributions. Finally, Gumbel's extreme value distribution is described – a derivation is given on the website. MATLAB and R functions for cdfs and quantiles of pdfs are used throughout the Chapter. The chapter ends with: a summary of: notation used; the main results, MATLAB and R syntax; and exercises.
