RewTransDistribution: Reward transformation

In aumath-advancedr2019/PhaseTypeGenetics: The Phase-Type Distribution with Applications in Population Genetics

Description

Reward transforming a continuous phase-type distribution with initial distribution initDist and sub-intensity rate matrix T_Mat.

Usage

RewTransDistribution(object, rewards)

Arguments

object	a continuous phase-type distributed object of class contphasetype.
rewards	a non-negative reward vector. The length of the reward vector should be equal to the number of rows of the sub-intensity rate matrix T_Mat.

Details

It is possible to assign a linear (non-negative) reward to each of the transient states of the Markov jump process underlying the phase-type distribution under consideration. More precisely, a reward is earned in each transient state and that reward is proportional to the time spent in the state. By assigning rewards, the original phase-type distribution is transformed into another continuous phase-type distribution. More details on the reward transformation can be found in vignette("PhaseTypeGenetics") or in Mogens Bladt and Bo Friis Nielsen (2017): Matrix-Exponential Distributions in Applied Probability.

Value

The function returns the reward transformed phase-type distribution, which is again an object of type contphasetype.

Source

Mogens Bladt and Bo Friis Nielsen (2017): Matrix-Exponential Distributions in Applied Probability. Probability Theory and Stochastic Modelling (Springer), Volume 81.

Examples

## The time to the most recent common ancestor (T_MRCA)
## is phase-type distributed with initial distribution
initDist <- c(1,0,0,0)
## and sub-intensity rate matrix
T_Mat <- matrix(c(-6,6,0,0,
                  0,-3,2,1,
                  0,0,-1,0,
                  0,0,0,-1), nrow = 4, byrow = TRUE)
## Defining an object of type "contphasetype"
TMRCA <- contphasetype(initDist, T_Mat)
## In order to obtain the distribution of the total
## length of all branches giving rise to singletons,
## we have to give the following rewards to the
## different states
r.vec <- c(4,2,1,0)
## Hence,
RewTransDistribution(TMRCA,r.vec)

aumath-advancedr2019/PhaseTypeGenetics documentation built on Dec. 3, 2019, 7:16 a.m.