Specifications

The toolbox provides nonlinear fitting func-
tions for classification and regression trees
and for nonlinear least squares. Using non-
linear least square functions, you can:
• Estimate parameters
• Interactively visualize and predict
multidimensional nonlinear fitting
• Set confidence intervals for parameters and
predicted values
You can also use the toolbox to work with
Hidden Markov models. You can estimate
the parameters of a model using the Baum-
Welch algorithm, calculate the most likely
path through a model using the Viterbi algo-
rithm, and generate random sequences from
a given model.
Probability Distributions
The Statistics Toolbox includes interac-
tive graphical user interfaces (GUIs) and
command-line tools that make it easy to look
at probability distributions, fit them to your
data, or generate random samples from them.
Graphical User Interfaces
The Distribution Fitting Tool is a GUI that
enables you to learn about a variety of prob-
ability distributions—for example, you can
graph a probability density function or
cumulative distribution function and investi-
gate how a distribution’s parameters affect its
position and shape.
The Distribution Fitting Tool lets you fit data
using 16 predefined probability distributions, a
nonparametric (kernel smoothing) estimator,
or a custom distribution that you define your-
self. It supports both complete and censored
(reliability) data and lets you exclude data, save
and load sessions, and generate M-code.
A second 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.
Command-line Functions
From the command line, you can perform
the following additional tasks:
• Calculate the probability density function (pdf)
• Calculate the cumulative distribution func-
tion (cdf) and its inverse
• Compute mean and variance
• Generate random numbers (such as noise
simulation)
• Estimate parameters
The Statistics Toolbox also includes functions
for generating random samples from multi-
variate distributions, such as t, normal, and
Wishart; sampling from finite populations;
and performing Latin hypercube sampling.
Linear and Nonlinear Modeling
The linear and nonlinear models provided
in the Statistics Toolbox let you model a
response variable as a function of one or
more predictor variables. These models make
predictions, establish relationships between
variables, or simplify a problem. For example,
linear and nonlinear regression models help
establish which variables have the most
impact on a response. Robust regression
methods can help you find outliers and
reduce their effect on the fitted model.
The toolbox provides linear algorithms for:
• One-way, two-way, and multiway ANOVA
• Mixed random and fixed-effects ANOVA
• Polynomial, stepwise, ridge, robust, and
multiple linear regression
• Generalized linear models
• Response surface fitting
Left: A matrix of scatter plots and
histograms comparing automobile
performance over three model
years. The Statistics Toolbox makes
it easy to plot multiple variables
and compare data.
Right: A parallel coordinates plot of multi-
variate data describing throttle performance.
The Statistics Toolbox provides convenient
tools for visualizing high dimensional data.