PXt {modesto}

Tool to computate the transient probability distribution for a Continuous Time Markov Chain, CTMC.

Description

Pt is used to obtain the transient probability distribution of a homogeneous continuous time Markov chain at a point of time t.

Usage

PXt(X0, R, t, epsilon = 0.001)

Arguments

X0

numeric vector, represents the probability distribution of the initial state.

R

numeric, represents the rate matrix of a CTMC.

t

numeric, represents the length of time.

epsilon

numeric, represents the error bound of the approximation of P(t). Default values is 0.001.

Author(s)

Carlos Alberto Cardozo Delgado <[e-mail]>.

References

Ross, S, Introduction to Probability Models, Eleven Edition. Academic Press, 2014.

Kulkarni V, Introduction to modeling and analysis of stochastic systems. Second Edition. Springer-Verlag, 2011.

Examples

library(modesto)
# A three states CTMC example
R <- matrix(c(0,2,0,3,0,1,0,6,0),3,3,byrow=TRUE)
X0 <- c(1,0,0)
PXt(X0,R,t=0.5,epsilon=0.005)
X0 <- c(0,0,1)
PXt(X0,R,t=0.5,epsilon=0.005)