3 - Statistical Distributions

Summary

This chapter describes the characteristics of the major probability distributiions used in the sciences, and serves as a compendium of information about them for reference purposes.It also introduces their implementation in Matlab. The treatment is separated into discrete and continuous cases. The binomial distribution that characterizes the number of successes in a fixed number of trials is defined. The negative binomila, multinomial and hypergeometric distributions are reviewed. The Poisson distribution is derived from the binomal, and characterizes rare discrete events. The important Gaussian distribution is treated thorougly, and its genearalization through the stable distribution familiy is defined. The Rayleigh, lognormal, Weibull, beta and extreme value distributions are described, and the gamma distribution family and its important exponential member are elucidated.The bivariate Gaussian distribution is derived. Finally, the von Mises and Fisher distributions of direction on the unit circle and sphere are obtained from first principles.