generator_functions {PhaseTypeR}

The phase-type distribution

Description

Generator functions for the S3 classes cont_phase_type, disc_phase_type, mult_cont_phase_type, mult_disc_phase_type, which represent the different phase-type distributions.

Usage

PH(subint_mat = NULL, init_probs = NULL)

DPH(subint_mat = NULL, init_probs = NULL)

MPH(subint_mat = NULL, init_probs = NULL,
    reward_mat = NULL)

MDPH(subint_mat = NULL, init_probs = NULL,
     reward_mat = NULL)

Arguments

subint_mat

a square matrix containing the transition rates or probabilities between transient states for continuous or discrete phase-type respectively. If the phase-type is continuous, the sub-intensity matrix diagonal should only contain negative values and the row sums should be non-positive. If the phase-type is discrete, the sub-intensity matrix should only contain values between 0 and 1.

init_probs

a vector, a one-row matrix or NULL which gives the probabilities to start in each state. If init_probs is NULL, the probability to start on the first state will be 1 and 0 otherwise.

reward_mat

a matrix NULL(default) where each row is a reward vector, and each column corresponds to a state. It should have the same number of columns as the length of the initial probabilities.

Details

PH, DPH, MPH and MDPH are the generator functions for the four types of phase-type distribution classes, this is, the continuous univariate, the discrete univariate, the continuous multivariate and the discrete multivariate respectively. The class is generated by supplying a sub-intensity matrix and an optional initial probability vector plus a reward matrix in the case of multivariate phase-type. If the initial probabilities are not specified, then the initial probability will be init_probs = c(1, 0, 0, ...) with the same length as the number of transient states.

Value

A phase-type object of class cont_phase_type for PH, disc_phase_type for DPH, mult_cont_phase_type for MPH, and mult_disc_phase_type for MDPH. All these classes inherit from list.

Examples

##===========================##
## For continuous univariate ##
##===========================##

subintensity_matrix <- matrix(c(-1.5, 1.5, 0,
                                 0,  -1,   1,
                                 0,   0,  -0.5),
                              ncol = 3,
                              byrow = TRUE)
PH(subintensity_matrix)

#---

subintensity_matrix <- matrix(c(-1.5, 1.5, 0,
                                 0,  -1,   1,
                                 0,   0,  -0.5),
                              ncol = 3,
                              byrow = TRUE)
initial_probabilities <- c(0.9, 0.1, 0)
PH(subintensity_matrix, initial_probabilities)


##=========================##
## For discrete univariate ##
##=========================##

subintensity_matrix <- matrix(c(0.4, 0.24, 0.12,
                                0,   0.4,  0.2,
                                0,   0,    0.5),
                              ncol = 3,
                              byrow = TRUE)
DPH(subintensity_matrix)

#---

subintensity_matrix <- matrix(c(0.4, 0.24, 0.12,
                                0,   0.4,  0.2,
                                0,   0,    0.5),
                              ncol = 3,
                              byrow = TRUE)
initial_probabilities <- c(0.9, 0.1, 0)
DPH(subintensity_matrix, initial_probabilities)



##=============================##
## For continuous multivariate ##
##=============================##

subintensity_matrix <- matrix(c(-3,  2,  0,
                                 0, -2,  1,
                                 0,  0, -1),
                              nrow = 3,
                              byrow = TRUE)
reward_matrix = matrix(sample(seq(0, 10, 0.1), 6), nrow = 3, ncol = 2)
initial_probabilities = c(1, 0, 0)
MPH(subintensity_matrix,
    initial_probabilities,
    reward_matrix)


##===========================##
## For discrete multivariate ##
##===========================##

subintensity_matrix <- matrix(c(0.4, 0.24, 0.12,
                                0,   0.4,  0.2,
                                0,   0,    0.5),
                              ncol = 3,
                              byrow = TRUE)
reward_matrix <- matrix(sample(seq(0, 10), 6), nrow = 3, ncol = 2)
initial_probabilities = c(1, 0, 0)
MDPH(subintensity_matrix,
     initial_probabilities,
     reward_mat = reward_matrix)