bd_equi: Equilibrium distribution of the jump chain of a linear...

In paulnorthrop/stat2003: stat2003: Introduction to Applied Probability at UCL

Description

bd_equi is used to find the equilibrium distribution of the jump chain of the input process.

Usage

bd_equi(BD, showstate = 0)

Arguments

BD	is an object in class 'stat2003.bd'
showstate	If there is so many state space, and you just want to take first n elements of the equilibrium distribution, then setting showstate = n. If showstate = 0, bd_equi will return whole equilibrium distribution. Default value of showstate is zero.

Details

In continuous time M.C.. If X (t), t >= 0 is an irreducible continuous-time Markov chain. If there exists an invariant distribution pi then it is unique, and the pi is also the equilibrium distribution of the chain. If there is no invariant distribution, then no equilibrium distribution exists. And When a process is not irreducible, cannot guarantee that an invariant distribution is an equilibrium distribution.

Value

bd_equi will return a vector if the process has equilibrium distribution.

See Also

stat2003.bd-class A class type of linear birth-death in stat2003 package.

bd_rate will return the generator matrix by given birth-death rates for a linear birth death process.

bd_trans will return the transition matrix by given birth-death rates for a linear birth death process.

bd_simu simulates a finite statespace Birth-death process by returning a plot about states and time.

Examples

A <- new("stat2003.bd", lb = 1, ld = 1, im = 3, em = 4,
nstate = 0)

bd_equi(A, 10)

paulnorthrop/stat2003 documentation built on May 24, 2019, 10:31 p.m.