Statistics Toolbox 7.2

Probability Distributions

Statistics Toolbox includes an extensive library of probability distribution functions that let you fit probability distributions to your data, compute functions from them, and generate random samples. From the command line you have access to more than 150 functions for:

• Generating random and quasi-random point sets
• Calculating the probability density function (pdf)
• Calculating the cumulative distribution function (cdf) and its inverse
• Computing mean and variance
• Estimating distribution parameters

Statistics Toolbox includes three interactive graphical user interfaces (GUIs) that simplify common analysis tasks. The Distribution Fitting Tool GUI lets you fit data using 23 predefined probability distributions, a nonparametric (kernel-smoothing) estimator, or a custom distribution that you define yourself. It supports both complete and censored (reliability) data and lets you exclude data, save and load sessions, and generate MATLAB code.

The Distribution Tool GUI lets you learn about a variety of probability distributions and explore how various parameters affect their position and shape.

The Random Number Tool GUI provides a random number generator to simulate behavior associated with particular distributions. You can use this random data to test hypotheses or models under different conditions, as well as perform Monte Carlo simulations.

Statistics Toolbox also includes functions for generating random samples from multivariate distributions, such as t, normal, copulas, and Wishart; sampling from finite populations; performing Latin hypercube sampling; and generating samples from Pearson and Johnson systems of distributions.

Statistics Toolbox can also fit parametric copulas to data, providing a link between models that describe marginal distribution and models that describe data correlations.

Analysis of Variance

Analysis of variance (ANOVA) lets you determine whether data sets from different groups have different characteristics. You can classify groups using discrete predictor variables. A follow-up multiple comparison analysis can pinpoint which pairs of groups differ from each other.

Statistics Toolbox includes algorithms for ANOVA and related techniques, including:

• One-way ANOVA with graphics
• Two-way ANOVA for balanced data
• Multiway ANOVA for balanced and unbalanced data (both fixed and random effects)
• Multivariate ANOVA
• Nonparametric one- and two-way ANOVA (Kruskal-Wallis, Friedman)
• Analysis of covariance (ANOCOVA)
• Multiple comparison of group means, slopes, and intercepts

Analysis of covariance (ANOCOVA) tool, which plots data to assess group-to-group differences and the impact of a predictor variable on a response variable. Click on image to see enlarged view.