R: Markov Modulated Poisson Process Object

mmpp {HiddenMarkov} | R Documentation

## Markov Modulated Poisson Process Object

### Description

Creates a Markov modulated Poisson process model object with class `"mmpp"`.

### Usage

    mmpp(tau, Q, delta, lambda, nonstat = TRUE)

### Arguments

`tau` | vector containing the event times. Note that the first event is at time zero. Alternatively, `tau` could be specified as `NULL`, meaning that the data will be added later (e.g. simulated).
`Q` | the infinitesimal generator matrix of the Markov process.
`delta` | is the marginal probability distribution of the m hidden states at time zero.
`lambda` | a vector containing the Poisson rates.
`nonstat` | is logical, `TRUE` if the homogeneous Markov process is assumed to be non-stationary, default.

### Details

The Markov modulated Poisson process is based on a hidden Markov process in continuous time. The initial state probabilities (at time zero) are specified by `delta` and the transition rates by the `Q` matrix. The rate parameter of the Poisson process (`lambda`) is determined by the current state of the hidden Markov process. Within each state, the Poisson process is homogeneous (constant rate parameter). A Poisson event is assumed to occur at time zero and at the end of the observation period, however, state transitions of the Markov process do not necessarily coincide with Poisson events. For more details, see Ryden (1996).

### Value

A `list` object with class `"mmpp"`, containing the above arguments as named components.

### References

Cited references are listed on the HiddenMarkov manual page.

### Examples

    Q <- matrix(c(-2,  2,
                   1, -1),
                byrow=TRUE, nrow=2)/10

    #    NULL indicates that we have no data at this point
    x <- mmpp(NULL, Q, delta=c(0, 1), lambda=c(5, 1))

    x <- simulate(x, nsim=5000, seed=5)

    y <- BaumWelch(x)

    print(summary(y))

    #    log-likelihood using initial parameter values
    print(logLik(x))

    #    log-likelihood using estimated parameter values
    print(logLik(y))

[Package HiddenMarkov version 1.8-8 Index]