Matvec Users’ Guide

13.3. DISCRETE DISTRIBUTION 105
Matvec interface
An object of P (λ) can be created by
D = StatDist("Poisson",lambda);
Matvec provided several standard member functions to allow user to access most of properties and
functions of P (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).
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 λ.
mean D.mean() returns the expected value.
variance D.variance() returns the variance.
Examples
> D = StatDist("Poisson",10)
PoissonDist(10)
> D.sample(1000).mean()
10.199
> D.sample(1000).variance()
9.98214
> D.pdf([0,10,100])
Col 1 Col 2 Col 3
Row 1 4.53999e-05 0.125110 4.86465e-63
> D.cdf([0,10,100])
Col 1 Col 2 Col 3
Row 1 4.53999e-05 0.583040 1.00000
> D.inv(0.5)
***ERROR***
PoissonDist::inv(): not available
13.3.3 Geometric distribution
Definition
The random variable X has a geometric distribution if its probability density function (pdf) is defined by
f(x) = (1 − p) x p, x = 0, 1, 2, . . . , (13.16)
where p (real) is the parameter with its range 0 ≤ p ≤ 1. In short, we say X ∼ g(p).
For example, let X be the number of failures before the first success in a sequence of Bernoulli trials with
probability of success p, then X ∼ g(p).