Matvec Users’ Guide

94 CHAPTER 13. STATISTICAL DISTRIBUTIONS
Matvec interface
An object of χ 2 (r, λ) can be created by
D = StatDist("ChiSquare",r,lambda);
D = StatDist("ChiSquare",r);
Matvec provided several standard member functions to allow user to access most of properties and
functions of χ 2 (r, λ):
pdf D.pdf(x) returns the probability density function (pdf) values of x which could be a vector or matrix.
cdf D.cdf(x) returns the cumulative distribution function (cdf) values of x which could be a vector or
matrix
mgf D.mgf(t) returns the moment-generating function (mgf) values of t which could be a vector or matrix.
inv D.inv(p) is the inverse function of D.cdf(x), where p could be a vector or matrix. That is if p =
D.cdf(x), then x = D.inv(p).
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(1) returns r, degree of freedom.
mean D.mean() returns the expected value of X ∼ χ 2 (r, λ).
variance D.variance() returns the variance of X ∼ χ 2 (r, λ).
Examples
> D = StatDist("ChiSquare",10,0.1)
ChiSquareDist(10,0.1)
> D.mean()
10.1
> D..sample(1000).mean()
10.0323
> D.pdf(5)
***ERROR***
ChiSquareDist::pdf(): not available yet: non-centrality
> D.cdf([0,1,10])
Col 1 Col 2 Col 3
Row 1 0.00000 0.000164396 0.550770
> D.inv([0,0.000164396,0.550770])
Col 1 Col 2 Col 3
Row 1 0.00000 1.00000 10.0000
> D.nonct(10,0.550770)
0.100003
> D.sample()
5.15093