Basic Statistics

Abstract

A stochastic variable is a combination of two components of deterministic variable, D, and random variable, ε. While D could be modeled by a range of mathematical models, ε is described by the probability theory using probability distribution function (pdf). Regarding the type of a random variable which might be discrete or continuous, it is defined by two types of discrete and continuous pdfs. Discrete distribution functions of Bernoulli, binomial, and Poisson are reviewed in this chapter along with the continuous distribution functions of exponential, uniform, normal, and extreme value. One of the most applicable fields of distribution functions is frequency analysis which is discussed in another section of this chapter. As far as the statistical analysis of real problems is concerned, hypothetical tests are widely used for deciding on either the parameters of one or several populations or the type of a distribution function which better fits the data. The hypothetical tests follow a general approach while that approach should be adapted for specific problems by defining appropriate statistical and critical values. The tests on the statistical parameters of populations are reviewed in this chapter. Furthermore, two famous tests of chi-square and Kolmogorov–Smirnov are presented to decide on the best distribution function for a specific random variable. Each of the above calculations is supported by the related commands and programs provided in MATLAB.