# PhaseTypeR: general-purpose phase-type functions

This package implements core functions from phase-type theory. Its general functions are useful for a wide-ranging variety of contexts. `PhaseTypeR` can be used to model continuous and discrete phase-type distributions, both univariate and multivariate. The package includes functions for outputting the mean and (co)variance of phase-type distributions; their density, probability and quantile functions; functions for random draws; functions for reward-transformation; and functions for plotting the distributions as networks.

## Installation

You can install `PhaseTypeR` from CRAN via:

``install.packages("PhaseTypeR")``

If you install devtools in your R environment with `install.packages("devtools")`, the development version of the package can be installed with the following command:

``devtools::install_github("rivasiker/PhaseTypeR")``

## Basic example

This is a basic example for the univariate continuous phase-type distribution.

``````# Load the package
library(PhaseTypeR)

# Define the sub-intensity rate matrix
subintensity_matrix <- matrix(c(-1.5,  0,  0,
1.5, -1,  0,
0,   1, -0.5), ncol = 3)
# Define the initial probabilities
initial_probabilities <- c(0.9, 0.1, 0)

# Create continuous phase-type object
ph <- PH(subintensity_matrix, initial_probabilities)``````

Summary of the object:

``````summary(ph)
#>
#> Subintensity matrix:
#>      [,1] [,2] [,3]
#> [1,] -1.5  1.5  0.0
#> [2,]  0.0 -1.0  1.0
#> [3,]  0.0  0.0 -0.5
#>
#> Initial probabilities:
#>      [,1] [,2] [,3]
#> [1,]  0.9  0.1    0
#>
#> Defect:
#>  0
#>
#> Mean: 3.6
#>
#> Variance: 5.44``````

Density function:

``````dPH(1:5, ph)
#>  0.1506327 0.2216989 0.1991321 0.1482987 0.1009037``````

Cumulative density function:

``````pPH(1:5, ph)
#>  0.07030638 0.26728005 0.48232823 0.65658059 0.78032198``````

Quantile function:

``````qPH(c(0.25, 0.5, 0.75), ph)
#>  1.921862 3.089664 4.716588``````

Random sampling:

``````set.seed(0)
rPH(6, ph)
#>  4.648661 6.111533 4.586241 5.708529 8.354549 5.768456``````

You can check out the full functionality of `PhaseTypeR` and its application to population genetics in the following guides: