Matvec Users’ Guide

Chapter 13
Statistical Distributions
13.1 Introduction
An object of StatDist class can be created as below:
D = StatDist("name",parameter-list)
where
1. name is one of the followings: Uniform, Normal, ChiSquare, t, F, Gamma, Exponential, Beta, DiscreteUniform,
Poisson, Binomial, NegativeBinomial, Geometric. Hypergeometric, Logistic, Laplace,
InverseGaussian, Cauchy, Weibull, Erlang will be added into the list.
2. parameter-list is a list of scalar values required by the corresponding distribution.
Note that some distributions have their non-centrality parameters. The non-centrality parameter is
always the last one in the parameter list. It is automatically set to zero if users don’t provide it explicitly.
There are nine member functions available now.
pdf D.pdf(x) returns the probability density function values of x which could be a vector or matrix.
cdf D.cdf(x) returns the cumulative distribution function values of x which could be a vector or matrix
mgf D.mgf(t) returns the moment-generating function values of t which could be a vector or matrix.
inv x = D.inv(p) is the inverse function of D.cdf(x), where p could be a vector or matrix.
nonct D.nonct(cv,p) returns non-centrality value given the critical value (cv) and p value (cdf). Both cv and
p could be either vector or matrix as long as the sizes are the same.
sample D.sample(), D.sample(n), and D.sample(m,n) return a random scalar or a vector of size n or a matrix
of size m by n.
parameter D.parameter(i) returns the i’th parameter of the distribution.
mean D.mean() returns the first moment (expected value) of the distribution.
variance D.variance() returns the second central moment (variance) of the distribution.
Here are two examples:
> N = StatDist("Normal",0, 10);
> B = StatDist("Binomial",2, 0.1);
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