IndTestPP (version 3.0)

SpecGap: Stationary distribution of a matrix and its spectral gap

Description

This function calculates the stationary distribution of the transition matrix of a Markov chain process and its spectral gap.

Usage

SpecGap(P)

Arguments

P

Matrix. It must be a markovian matrix.

Value

A list with elements

SG

Spectral gap value of the matrix.

pi

Vector of the stationary distribution of the matrix.

Details

The spectral gap of a matrix \(P\) measures the convergence speed of \(P\) to a matrix \(P_I\) with all the rows equal to \((\pi_1,\pi_2,... \pi_k)\), the stationary distribution of \(P\). It takes values in [0,1].

The spectral gap of a transition matrix can be used as a dependence measure between the marginal processes defined by a marked Poisson procces with discrete marks generated by a Markov chain with that transition matrix, see Cebrian et al (2020) for details.

References

Cebrian, A.C., Abaurrea, J. and Asin, J. (2020). Testing independence between two point processes in time. Journal of Simulation and Computational Statistics.

See Also

DepNHPPMarked

Examples

# NOT RUN {
P<-cbind(c(0.7, 0.1, 0.2), c(0.2, 0.7, 0.1), c(0.1, 0.2, 0.7))
SpecGap(P)
# }