statdis {RIPSeeker} | R Documentation

## Returns the stationary distribution of a Markov chain.

### Description

Given a transition matrix A, returns the stationary distribution of a Markov chain by computing the eigen vectors of A.

### Usage

    statdis(A)

### Arguments

`A` | Transition probability matrix, a squared matrix of probabilities (0 ≤ p ≤ 1) with row and column length equal to that of alpha and beta and row sum and column sum both equal to 1 (within some numerical deviation of 1e-6).

### Value

`w` | Stationary weights for the distributions of K components based on the transition probability matrix.

### Author(s)

Yue Li

### References

Capp\'e, O. (2001). H2M : A set of MATLAB/OCTAVE functions for the EM estimation of mixtures and hidden Markov models. (http://perso.telecom-paristech.fr/cappe/h2m/)

### See Also

`nbh_em`

### Examples

    # Simulate data
    TRANS_s <- matrix(c(0.9, 0.1, 0.3, 0.7), nrow=2, byrow=TRUE)
    alpha_s <- c(2, 4)
    beta_s  <- c(1, 0.25)
    Total <- 100

    x <- nbh_gen(TRANS_s, alpha_s, beta_s, Total);

    count <- x$count
    label <- x$label

    Total <- length(count)

    # dummy initialization
    TRANS0 <- matrix(rep(0.5,4), 2)

    alpha0 <- c(1, 20)

    beta0 <- c(1, 1)

    NIT_MAX <- 50
    TOL <- 1e-100
    nbh <- nbh_em(count, TRANS0, alpha0, beta0, NIT_MAX, TOL)

    map.accuracy <- length(which(max.col(nbh$postprob) == label))/Total

    vit <- nbh_vit(count, nbh$TRANS, nbh$alpha, nbh$beta)

    vit.accuracy <- length(which(vit$class == label))/Total

    # Plot the marginal distribution (in the stationnary regime)
    # Compute negative binomial distributions for all model states
    t <- 0:max(count)

    tmp <- nbh_em(t, nbh$TRANS, nbh$alpha, nbh$beta, 1)

    dens <- tmp$dens

    w <- statdis(nbh$TRANS)

    # Plot estimate of marginal probabilities
    marprob <- apply(t(dens) * (t(w) %*% matrix(1, ncol=length(t))), 2, sum)

    plot(t, marprob, pch=8, col="blue", main="Estimated marginal distribution")

    # Plot empirical estimated probabilities
    dhist <- matrix(0, ncol=length(t))

    for(i in t){
    	dhist[1+i] <- sum(count == i)/Total
    }

    points(t, dhist, pch=3, col="red")

[Package RIPSeeker version 1.20.0 Index]