Canonical Form 1 for Phase-Type (PH) Distribution

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Description

A function to generate an object of cf1.

Usage

1
cf1(size, alpha, rate, class = "CsparseMatrix")

Arguments

size

a value for the number of phases.

alpha

a vector for the initial probabilities of PH distribution.

rate

a vector for transition rates to next phase (diagonal elements of Q).

class

name of Matrix class for Q.

Details

The PH distribution with parameters α, Q and ξ = - Q 1: Cumulative probability function;

F(q) = 1 - α \exp( Q q ) 1

Probability density function;

f(x) = α \exp( Q x ) ξ,

where Q is a bidiagonal matrix whose entries are sorted.

Value

cf1 gives an object of canonical form 1 that is a subclass of PH distribution.

Note

rph is a generic function and is specified for cf1.

See Also

ph, herlang

Examples

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## create a CF1 with 5 phases
(param1 <- cf1(5))

## create a CF1 with 5 phases
(param1 <- cf1(size=5))

## create a CF1 with specific parameters
(param2 <- cf1(alpha=c(1,0,0), rate=c(1.0,2.0,3.0)))

## p.d.f. for 0, 0.1, ..., 1
(dph(x=seq(0, 1, 0.1), ph=param2))

## c.d.f. for 0, 0.1, ..., 1
(pph(q=seq(0, 1, 0.1), ph=param2))

## generate 10 samples (this is quiker than rph with general ph)
(rph(n=10, ph=param2))