This is a package for working with Phase-type (PHT) distributions in the R programming language. The entire of the MCMC portion of the code has been written in optimised C for higher performance and very low memory use, whilst being easy to call from wrapper R functions.
Consider a continuous-time Markov chain (CTMC) on a finite discrete state space of size \(n+1\), where one of the states is absorbing. Without loss of generality the generator of the chain can be written in the form:
\[\mathbf{T} = \left( \begin{array}{cc} \mathbf{S} & \mathbf{s} \\ \mathbf{0}^\mathrm{T} & 0 \end{array} \right)\]
where \(\mathbf{S}\) is the \(n \times n\) matrix of transition rates between non-absorbing states; \(\mathbf{s}\) is an \(n\) dimensional vector of absorption rates; and \(\mathbf{0}\) is an \(n\) dimensional vector of zeros. We take \(\boldsymbol{\pi}\) as the initial state distribution: an \(n\) dimensional vector of probabilities \(\left(\sum_i \pi_i=1\right)\) such that \(\pi_i\) is the probability of the chain starting in state \(i\).
Then, we define a Phase-type distribution to be the distribution of the time to absorption of the CTMC with generator \(\mathbf{T}\), or equivalently as the first passage time to state \(n+1\). Thus, a Phase-type distribution is a positively supported univariate distribution having distribution and density functions:
\[\begin{array}{rcl} F_X(x) &=& 1 - \boldsymbol{\pi}^\mathrm{T} \exp\\{x \mathbf{S}\\} \mathbf{e}\\ f_X(x) &=& \boldsymbol{\pi}^\mathrm{T} \exp\\{x \mathbf{S}\\} \mathbf{s} \end{array} \qquad \mbox{for } x \in [0,\infty)\]
where \(\mathbf{e}\) is an \(n\) dimensional vector of \(1\)’s; \(x\) is the time to absorption (or equivalently first-passage time to state \(n+1\)); and \(\exp\\{x \mathbf{S}\\}\) is the matrix exponential. We denote that a random variable \(X\) is Phase-type distributed with parameters \(\boldsymbol{\pi}\) and \(\mathbf{T}\) by \(X \sim \mathrm{PHT}(\boldsymbol{\pi},\mathbf{T})\).
Note that \(\displaystyle \sum_{j=1}^n S_{ij} = -s_i \ \forall\\,i\), so often a Phase-type is defined merely by providing \(\mathbf{S}\), \(\mathbf{T}\) then being implicitly known.
Please feel free to:
You can install the latest release directly from CRAN.
install.packages("PhaseType")You can get the very latest version from R-universe:
install.packages("PhaseType", repos = c("https://louisaslett.r-universe.dev", "https://cloud.r-project.org"))Installing directly from GitHub is
not supported by the install.packages command, but if you
wish to compile from source then you could use the devtools
package:
install.packages("remotes")
remotes::install_github("louisaslett/PhaseType")Under releases, the tree/commit from which CRAN releases were made are recorded, so historic source can be downloaded from there.
If you use this software, please use the following citation:
Aslett, L. J. M. (2012), MCMC for Inference on Phase-type and Masked System Lifetime Models, PhD thesis, Trinity College Dublin.
@phdthesis{Aslett2012,
title={MCMC for Inference on Phase-type and Masked System Lifetime Models},
author={Aslett, L. J. M.},
year={2012},
school={Trinity College Dublin}
}Thank-you :smiley: