Matvec Users’ Guide

13.2. CONTINUOUS DISTRIBUTION 97
Properties
1. E(X) = r2(r1+δ)
r 1(r 2−2) , for r 2 > 2
2. Var(X) = 2(r 2 /r 1 ) 2 (r 1+δ) 2 +(r 1+2δ)(r 2−2)
(r 2−2) 2 (r 2−4)
for r 2 > 4
Matvec interface
An object of F (r 2 , r 2 , δ) can be created by
D = StatDist("F",r1,r2,delta);
D = StatDist("F",r1,r2);
Matvec provided several standard member functions to allow user to access most of properties and
functions of F (r 1 , r 2 , δ):
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 1 , D.parameter(2) returns r 2 , and D.parameter(3) returns δ.
mean D.mean() returns the expected value.
variance D.variance() returns the variance.
Examples
> D = StatDist("F",5,100,0.5)
FDist(5,100,0.5)
> D.mean()
1.12245
> D.sample(1000).mean()
1.11399
> D.variance()
0.536452
> D.pdf(2)
***ERROR***
FDist::pdf(): not available yet: non-centrality
> D.cdf([0.1,1,3])
Col 1 Col 2 Col 3
Row 1 0.00642900 0.520762 0.976739
> D.inv([0.00642900,0.520762,0.976739])
Col 1 Col 2 Col 3
Row 1 0.100000 1.00000 3.00000