Add commutationNumbers function to calculate commutation numbers lx, dx, Dx,...

Add commutationNumbers function to calculate commutation numbers lx, dx, Dx, Nx, Sx, Cx, Mx, Rx  for a given mortality table or vector of death probabilities

DESCRIPTION

@@ -34,6 +34,8 @@ Collate:
     'ages.R'
     'baseTable.R'
     'baseYear.R'
+    'pensionTable.R'
+    'commutationNumbers.R'
     'mortalityTable.improvementFactors.R'
     'mortalityTable.trendProjection.R'
     'deathProbabilities.R'
@@ -51,7 +53,6 @@ Collate:
     'mortalityTable.jointLives.R'
     'mortalityTables.list.R'
     'mortalityTables.load.R'
-    'pensionTable.R'
     'plot.mortalityTable.R'
     'plotMortalityTableComparisons.R'
     'plotMortalityTables.R'

NAMESPACE

@@ -43,6 +43,7 @@ exportMethods(ages)
 exportMethods(baseTable)
 exportMethods(baseYear)
 exportMethods(calculateImprovements)
+exportMethods(commutationNumbers)
 exportMethods(deathProbabilities)
 exportMethods(getCohortTable)
 exportMethods(getOmega)

R/commutationNumbers.R

+#' @include mortalityTable.R pensionTable.R
+NULL
+
+#' Calculate the commutation numbers for the given parameters, using the mortality table and an interest rate
+#'
+#' @param object The life table object (class inherited from mortalityTable)
+#' @param ... Other parameters to be passed to the deathProbabilities call (e.g. YOB)
+#' @param i Interest rate used for the calculation of the commutation numbers
+#'
+#' @examples
+#' mortalityTables.load("Austria_Annuities")
+#' commutationNumbers(AVOe2005R.male, i = 0.03, YOB = 1975)
+#'
+#' @exportMethod commutationNumbers
+setGeneric("commutationNumbers", function(object, ..., i = 0.03) standardGeneric("commutationNumbers"));
+
+#' @describeIn commutationNumbers Calculate the commutation numbers for the given
+#'             parameters, using the mortality table and an interest rate
+setMethod("commutationNumbers", "mortalityTable",
+          function(object, ..., i = 0.03) {
+              ages = ages(object, ...)
+              qx = deathProbabilities(object, ...)
+              commutationNumbers(qx, ages, i)
+          })
+
+
+#' @describeIn commutationNumbers Calculate the commutation numbers for the given
+#'             death probabilities (passed as a numeric vector with argument
+#'             name "object"), ages and an interest rate
+#'             Return value is a list of data frames
+setMethod("commutationNumbers", "numeric",
+          function(object, ages, i = 0.03) {
+              v = 1/(1 + i)
+              lx = cumprod(c(100000, 1 - object[-length(object)]))
+              dx = -diff(c(lx, 0))
+              Dx = v^ages * lx
+              Nx = rev(cumsum(rev(Dx))) # Nx is sum of Dx from x to omega
+              Sx = rev(cumsum(rev(Nx))) # Sx is sum of Nx from x to omega
+
+              Cx = qx * v * Dx
+              Mx = rev(cumsum(rev(Cx)))
+              Rx = rev(cumsum(rev(Mx)))
+
+              data.frame(age = ages, qx, lx, dx, Dx, Nx, Sx, Cx, Mx, Rx)
+          })
+
+#' @describeIn commutationNumbers Calculate the commutation numbers for the given
+#'             parameters, using the pension table and an interest rate
+#'             Return value is a list of data frames
+setMethod("commutationNumbers", "pensionTable",
+          function(object, ..., i = 0.03) {
+              probs = transitionProbabilities(object, ...)
+              ages = probs$x
+              list(
+                  q  = commutationNumbers(probs$q,  ages = ages, i = i),
+                  qi = commutationNumbers(probs$qi, ages = ages, i = i),
+                  qp = commutationNumbers(probs$qp, ages = ages, i = i),
+                  qw = commutationNumbers(probs$qw, ages = ages, i = i),
+                  qg = commutationNumbers(probs$qg, ages = ages, i = i)
+              )
+          })
+
+
+# commutationNumbers(deathProbabilities(AVOe2008P.male@qpx, YOB = 1982), ages(AVOe2008P.male@qpx), i = 0.06)
+# commutationNumbers(AVOe2008P.male@qpx, i = 0.06, YOB = 1982) %>% View
+
+# AVOe2008P.male.Comm = commutationNumbers(AVOe2008P.male, i = 0.06, YOB = 1982)
+# AVOe2008P.male.Comm[["q"]] %>% View
+# AVOe2008P.male.Comm[["qi"]] %>% View
+# AVOe2008P.male.Comm[["qp"]] %>% View
+# AVOe2008P.male.Comm[["qw"]] %>% View
+# AVOe2008P.male.Comm[["qg"]] %>% View

man/commutationNumbers.Rd

+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/commutationNumbers.R
+\docType{methods}
+\name{commutationNumbers}
+\alias{commutationNumbers}
+\alias{commutationNumbers,mortalityTable-method}
+\alias{commutationNumbers,numeric-method}
+\alias{commutationNumbers,pensionTable-method}
+\title{Calculate the commutation numbers for the given parameters, using the mortality table and an interest rate}
+\usage{
+commutationNumbers(object, ..., i = 0.03)
+
+\S4method{commutationNumbers}{mortalityTable}(object, ..., i = 0.03)
+
+\S4method{commutationNumbers}{numeric}(object, ages, i = 0.03)
+
+\S4method{commutationNumbers}{pensionTable}(object, ..., i = 0.03)
+}
+\arguments{
+\item{object}{The life table object (class inherited from mortalityTable)}
+
+\item{...}{Other parameters to be passed to the deathProbabilities call (e.g. YOB)}
+
+\item{i}{Interest rate used for the calculation of the commutation numbers}
+}
+\description{
+Calculate the commutation numbers for the given parameters, using the mortality table and an interest rate
+}
+\section{Methods (by class)}{
+\itemize{
+\item \code{mortalityTable}: Calculate the commutation numbers for the given
+parameters, using the mortality table and an interest rate
+
+\item \code{numeric}: Calculate the commutation numbers for the given
+death probabilities (passed as a numeric vector with argument
+name "object"), ages and an interest rate
+Return value is a list of data frames
+
+\item \code{pensionTable}: Calculate the commutation numbers for the given
+parameters, using the pension table and an interest rate
+Return value is a list of data frames
+}}
+
+\examples{
+mortalityTables.load("Austria_Annuities")
+commutationNumbers(AVOe2005R.male, i = 0.03, YOB = 1975)
+
+}