ProjectMindmap/MeanAndVariance.R

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

##----------------------------------------------------
## The mean of a continuous phase-type distribution
##----------------------------------------------------
## Name: mean_contphasetype
## Purpose: Computing the mean of a continuous phase-
##          type distribution (Corollary 1.2.64 in [BN])
## Input:
## initDist = the initial distribution
## T.mat = the subintensity matrix from the
##        continuous phase type distribution
## Output:
## The mean E[tau]
##----------------------------------------------------

mean_contphasetype <- function(initDist, T.mat){

  return(sum(initDist%*%solve(-T.mat)))

}

##----------------------------------------------------
## The mean of a continuous phase-type distribution
##----------------------------------------------------
## Name: mean.contphasetype
## Purpose: Computing the mean of a continuous phase-
##          type distribution (Corollary 1.2.64 in [BN])
## Input:
## cptd = the continuous phase-type distribution object
## Output:
## The mean E[tau]
##----------------------------------------------------

mean.contphasetype <- function(cptd){

  mean_contphasetype(initDist = cptd$initDist, T.mat= cptd$T.mat)

}

##----------------------------------------------------
## The mean of a discrete phase-type distribution
##----------------------------------------------------
## Name: mean_discphasetype
## Purpose: Computing the mean of a discrete phase-
##          type distribution (Corollary 1.2.64 in [BN])
## Input:
## T.mat = the subtransition matrix from the
##        discrete phase type distribution
## initDist = the initial distribution
## Output:
## The mean E[tau]
##----------------------------------------------------

mean_discphasetype <- function(dptd){

  return(sum(initDist%*%solve(diag(x=1, nrow = nrow(T.mat))-T.mat)) + 1 - sum(initDist))

}

##----------------------------------------------------
## The mean of a discrete phase-type distribution
##----------------------------------------------------
## Name: mean.discphasetype
## Purpose: Computing the mean of a discrete phase-
##          type distribution (Corollary 1.2.64 in [BN])
## Input:
## dptd = the discrete phase-type distribution object
## Output:
## The mean E[tau]
##----------------------------------------------------

mean.discphasetype <- function(dptd){
  mean_discphasetype(initDist = dptd$initDist, T.mat=dptd$T.mat)
}

## Defining a generic var() function

var <- function(...){

  UseMethod("var")
}

## The default
var.default <- function(x,...){

  var(x,...)
}


##----------------------------------------------------
## The variance of a discrete phase-type distribution
##----------------------------------------------------
## Name: var_discphasetype
## Purpose: Computing the variance of a discrete phase-
##          type distribution
##          (using Theorem 1.2.69 in [BN])
## Input:
## T.mat = the subtransition matrix from the
##        discrete phase type distribution
## initDist = the initial distribution
## Output:
## The variance Var[tau]
##----------------------------------------------------
var_discphasetype <- function(initDist, T.mat){
  defect <- 1 - sum(initDist)
  secondMoment <- 2*sum(initDist%*%T.mat%*%solve((diag(x=1, nrow = nrow(T.mat))-T.mat)%^%2))
  firstmoment <- sum(initDist%*%solve(diag(x=1, nrow = nrow(T.mat))-T.mat)) + defect
  return(secondMoment + firstmoment - firstmoment^2)
}

## The variance of a discrete phase-type distribution
##----------------------------------------------------
## Name: var.discphasetype
## Purpose: Computing the variance of a discrete phase-
##          type distribution
##          (using Theorem 1.2.69 in [BN])
## Input:
## dptd = the discrete phase-type distribution object
## Output:
## The variance Var[tau]
##----------------------------------------------------
var.discphasetype <- function(dptd){
  var_discphasetype(initDist = dptd$initDist, T.mat = dptd$T.mat)
}

##----------------------------------------------------
## The variance of a continuous phase-type distribution
##----------------------------------------------------
## Name: var_contphasetype
## Purpose: Computing the variance of a continuous
##          phase-type distribution
##          (using Theorem 1.2.69 in [BN])
## Input:
## T.mat = the subintensity matrix from the
##        continuous phase type distribution
## initDist = the initial distribution
## Output:
## The variance Var[tau]
##----------------------------------------------------
var_contphasetype <- function(initDist, T.mat){

  return(LaplacePhaseType(initDist = initDist, Tmat = T.mat, i=2)-
    LaplacePhaseType(initDist = initDist, Tmat = T.mat, i=1)^2)
}

##----------------------------------------------------
## The variance of a continuous phase-type distribution
##----------------------------------------------------
## Name: var.contphasetype
## Purpose: Computing the variance of a continuous
##          phase-type distribution
##          (using Theorem 1.2.69 in [BN])
## Input:
## cptd = the continuous phase-type distribution object which
## is a list with two entries
## cptd$T.mat = the subintensity matrix from the
##        continuous phase type distribution
## cptd$initDist = the initial distribution
## Output:
## The variance Var[tau]
##----------------------------------------------------
var.contphasetype <- function(cptd){
  var_contphasetype(initDist = cptd$initDist, T.mat = cptd$T.mat)
}