Density, probability distribution, quantile, moment, hazard and random number generation functions for the Coxian phase-type distribution with any number of phases.

Usage

dnphase(x, prate, arate, initp = NULL, method = "expm")

pnphase(q, prate, arate, initp = NULL, method = "expm", lower.tail = TRUE)

hnphase(x, prate, arate, initp = NULL, method = "expm")

mean_nphase(prate, arate, initp = NULL)

var_nphase(prate, arate, initp = NULL)

skewness_nphase(prate, arate, initp = NULL)

ncmoment_nphase(prate, arate, i, initp = NULL)

rnphase(n, prate, arate)

qnphase(p, prate, arate, lower.tail = TRUE, log.p = FALSE, method = "expm")

Arguments

x: Value at which to evaluate the PDF, CDF, or hazard.
prate: Progression rates. Either a vector of length nphase-1, or a matrix with npar rows and nphase-1 columns.
arate: Absorption rates. Either a vector of length nphase, or a matrix with npar rows and nphase columns.
initp: Vector of probabilities of occupying each phase at the start of the sojourn. By default, the first phase has probability 1.
method: If "analytic" then for nphase 5 or less, an analytic solution to the matrix exponential is employed in the calculation. For nphase 6 or more, or if method="mexp" the matrix exponential is determined using numerical methods, via expm::expm().
q: Value at which to evaluate the CDF.
lower.tail: If TRUE return P(X<x), else P(X>=x).
i: which moment to return from ncmoment_nphase
n: Number of random samples to generate, for rnphase. If prate or arate is a matrix with more than one row, its rows are recycled to length n and one random number is generated per row, in the same fashion as the mean and sd arguments of rnorm. In particular if n equals the number of rows of arate, then exactly one random number is generated for the parameters given by each row.
p: Probability at which to evaluate the quantile
log.p: return log probability

Value

A vector of length n or length(x).

Details

The number of phases, nphase, is taken from the dimensions of the object supplied as arate. If arate is a vector, then the number of phases is assumed to equal the length of this vector. If arate is a matrix, then the number of phases is assumed to be the number of columns.

mean_nphase, var_nphase, skewness_nphase and ncmoment_nphase return the mean, variance, skewness and general non-central moments of the distribution.

These functions work in a vectorised way, so that alternative parameter values or evaluation values x can be supplied. The number of alternative values is determined from the number of rows of arate. Then if necessary, prate and x are replicated to match the size of arate.