Matvec Users’ Guide

106 CHAPTER 13. STATISTICAL DISTRIBUTIONS
Properties
1. its moment generation function is
2. E(X) = 1−p
p
Matvec interface
, Var(X) =
1−p
p 2 .
An object of g(p) can be created by
D = StatDist("Geometric",p);
M(t) =
p
, t < − ln(1 − p)
1 − (1 − p)et Matvec provided several standard member functions to allow user to access most of properties and
functions of g(p):
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).
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 p, the probability of success in a Bernoulli trial.
mean D.mean() returns the expected value.
variance D.variance() returns the variance.
Examples
> D = StatDist("Geometric",0.2)
GeometricDist(0.2)
> D.mean()
4
> D.sample(1000).mean()
3.751
> D.pdf([1,2,10])
Col 1 Col 2 Col 3
Row 1 0.160000 0.128000 0.0214748
> D.cdf([1,2,10])
Col 1 Col 2 Col 3
Row 1 0.360000 0.488000 0.914101
> D.inv(0.5)
***ERROR***
GeometricDist::inv(): not available