modesto (version 0.1.4)

PXt: 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.

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

# NOT RUN {
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)

# }