Matvec Users’ Guide

13.2. CONTINUOUS DISTRIBUTION 101
Matvec interface
An object of Beta(α, β, λ) can be created by
D = StatDist("Beta",alpha,beta,lambda);
D = StatDist("Beta",alpha,beta);
Matvec provided several standard member functions to allow user to access most of properties and
functions of Beta(α, β, 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 α, D.parameter(2) returns β, and D.parameter(3) returns λ.
mean D.mean() returns the expected value.
variance D.variance() returns the variance.
Examples
> C = StatDist("Beta",2,3)
BetaDist(2,3,0)
> D.mean()
0.4
> D.sample(1000).mean()
0.407094
> D.pdf([0.01,0.5,0.9])
Col 1 Col 2 Col 3
Row 1 0.117612 1.50000 0.108000
> D.cdf([0.01,0.5,0.9])
Col 1 Col 2 Col 3
Row 1 0.000592030 0.687500 0.996300
> D.inv([0.000592030,0.687500,0.996300])
Col 1 Col 2 Col 3
Row 1 0.00999928 0.500001 0.900001
13.2.9 Log normal distribution
Definition
The random variable X has a lognormal distribution if its probability density function (pdf) is defined by
f(x) = [(x − θ) √ (2π)σ] −1 exp(−
log(x − θ) − µ)2
2σ 2 ), x > θ (13.13)