From e8bc098129f8ba726e03526535ae2a22883fa0f8 Mon Sep 17 00:00:00 2001
From: Reinhold Kainhofer <reinhold@kainhofer.com>
Date: Sun, 10 Sep 2017 20:59:56 +0000
Subject: [PATCH] Add analytic mortality distributions

- mortalityTable.deMoivre(omega)
- mortalityTable.MakehamGompertz(A, B, c)
- mortalityTable.Weibull(k, n)
---
 DESCRIPTION                                 |  3 +
 NAMESPACE                                   |  6 ++
 R/mortalityTable.MakehamGompertz.R          | 65 +++++++++++++++++++++
 R/mortalityTable.Weibull.R                  | 48 +++++++++++++++
 R/mortalityTable.deMoivre.R                 | 42 +++++++++++++
 man/mortalityTable.MakehamGompertz-class.Rd | 38 ++++++++++++
 man/mortalityTable.Weibull-class.Rd         | 32 ++++++++++
 man/mortalityTable.deMoivre-class.Rd        | 27 +++++++++
 8 files changed, 261 insertions(+)
 create mode 100644 R/mortalityTable.MakehamGompertz.R
 create mode 100644 R/mortalityTable.Weibull.R
 create mode 100644 R/mortalityTable.deMoivre.R
 create mode 100644 man/mortalityTable.MakehamGompertz-class.Rd
 create mode 100644 man/mortalityTable.Weibull-class.Rd
 create mode 100644 man/mortalityTable.deMoivre-class.Rd

diff --git a/DESCRIPTION b/DESCRIPTION
index 68fd0dd..e42b6b4 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -44,6 +44,9 @@ Collate:
     'makeQxDataFrame.R'
     'mortalityComparisonTable.R'
     'mortalityImprovement.R'
+    'mortalityTable.MakehamGompertz.R'
+    'mortalityTable.Weibull.R'
+    'mortalityTable.deMoivre.R'
     'periodDeathProbabilities.R'
     'mortalityTable.jointLives.R'
     'mortalityTables.list.R'
diff --git a/NAMESPACE b/NAMESPACE
index 38e64ed..698b724 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -6,7 +6,10 @@ export(generateAgeShift)
 export(makeQxDataFrame)
 export(mortalityComparisonTable)
 export(mortalityTable)
+export(mortalityTable.MakehamGompertz)
+export(mortalityTable.Weibull)
 export(mortalityTable.ageShift)
+export(mortalityTable.deMoivre)
 export(mortalityTable.improvementFactors)
 export(mortalityTable.joined)
 export(mortalityTable.jointLives)
@@ -26,7 +29,10 @@ export(plotMortalityTableComparisons)
 export(plotMortalityTables)
 export(plotMortalityTrend)
 exportClasses(mortalityTable)
+exportClasses(mortalityTable.MakehamGompertz)
+exportClasses(mortalityTable.Weibull)
 exportClasses(mortalityTable.ageShift)
+exportClasses(mortalityTable.deMoivre)
 exportClasses(mortalityTable.improvementFactors)
 exportClasses(mortalityTable.joined)
 exportClasses(mortalityTable.jointLives)
diff --git a/R/mortalityTable.MakehamGompertz.R b/R/mortalityTable.MakehamGompertz.R
new file mode 100644
index 0000000..7089136
--- /dev/null
+++ b/R/mortalityTable.MakehamGompertz.R
@@ -0,0 +1,65 @@
+#' @include mortalityTable.period.R
+NULL
+
+#' Class mortalityTable.MakehamGompertz - Mortality table with Makeham-Gompertz's law
+#'
+#' A period life table following Makeham and Gompertz's law of a mortality rate
+#' $\mu$ increasing exponentially with age $x$ ($\mu_{x+t} = A + B c^{(x+t)}$).
+#' The only required slots are the parameters $A$, $B$ and $c$, all probabilities
+#' are calculated from them, for technical reasons a maximum age of 120 is
+#' technically assumed.  Optionally, a name and loading can be passed
+#' (inherited from \code{\link{mortalityTable}}).
+#'
+#' @slot A          Parameter A of the Makeham-Gompertz distribution
+#' @slot B          Parameter B of the Makeham-Gompertz distribution
+#' @slot c          Parameter c of the Makeham-Gompertz distribution
+#' @slot omega      Maximum age (default: 150)
+#'
+#' @examples
+#' # A Gompertz mortality, roughtly approximating the Austrian annuitants 2017
+#' gmp = mortalityTable.MakehamGompertz(A = 0, B = 0.00001, c = 1.11)
+#' mortalityTables.load("Austria_Annuities_AVOe2005R")
+#' plot(gmp, AVOe2005R.male, Period=2017)
+#'
+#' # A Makeham-Gompertz mortality, approximating the Austrian annuitants 2017
+#' mg = mortalityTable.MakehamGompertz(A = 0.0002, B = 0.00001, c = 1.11)
+#' plot(mg, gmp, AVOe2005R.male, Period=2017)
+#'
+#' @export mortalityTable.MakehamGompertz
+#' @exportClass mortalityTable.MakehamGompertz
+mortalityTable.MakehamGompertz = setClass(
+    "mortalityTable.MakehamGompertz",
+    slots = list(
+        A = "numeric",
+        B = "numeric",
+        c = "numeric",
+        omega = "numeric"
+    ),
+    prototype = list(
+        A = 0,
+        B = 1,
+        c = 1,
+        omega = 120
+    ),
+    contains = "mortalityTable.period"
+)
+
+setMethod("initialize", "mortalityTable.MakehamGompertz", function(.Object, A = 0, B = 1, c = 1, omega = 120, name = NULL, ...) {
+    if (missing(name) || is.null(name)) {
+        if (A == 0) {
+            name = paste("Gompertz mortality, B=", B, ", c=", c, collapse = "")
+        } else if (B == 0 || c == 1) {
+            name = paste("Exponential mortality, mu=", A + B * c, collapse = "")
+        } else {
+            name = paste("Makeham-Gompertz mortality, A=", A, ", B=", B, ", c=", c, collapse = "")
+        }
+    }
+    ages = 0:omega
+    if (c == 1 || B == 0) {
+        deathProbs = 1 - exp(-A)
+    } else {
+        deathProbs = 1 - exp(-A) * exp(B/log(c) * (c^ages - c^(ages + 1)))
+    }
+    callNextMethod(.Object, A = A, B = B, c = c, omega = omega, name = name, ages = ages, deathProbs = deathProbs, ...)
+})
+
diff --git a/R/mortalityTable.Weibull.R b/R/mortalityTable.Weibull.R
new file mode 100644
index 0000000..8c7f666
--- /dev/null
+++ b/R/mortalityTable.Weibull.R
@@ -0,0 +1,48 @@
+#' @include mortalityTable.period.R
+NULL
+
+#' Class mortalityTable.Weibull - Mortality table with Weibull's law
+#'
+#' A period life table following Weibulls's law of a mortality rate
+#' $\mu$ increasing as a power of $t$ ($\mu_{x+t} = k * (x+t)^n$).
+#' The only required slots are the parameters $k>0$ and $n>0$, all probabilities
+#' are calculated from them, for technical reasons a maximum age of 150 is
+#' technically assumed.  Optionally, a name and loading can be passed
+#' (inherited from \code{\link{mortalityTable}}).
+#'
+#' @slot k          Parameter k of the Weibull distribution
+#' @slot n          Parameter n of the Weibull distribution
+#' @slot omega      Maximum age (default: 120)
+#'
+#' @examples
+#' # A Weibull mortality
+#' wbl = mortalityTable.Weibull(k = 0.0000000001, n = 4.8)
+#' mortalityTables.load("Austria_Annuities_AVOe2005R")
+#' plot(wbl, AVOe2005R.male, Period=2017, ylim = c(0.00005, 1))
+#'
+#' @export mortalityTable.Weibull
+#' @exportClass mortalityTable.Weibull
+mortalityTable.Weibull = setClass(
+    "mortalityTable.Weibull",
+    slots = list(
+        k = "numeric",
+        n = "numeric",
+        omega = "numeric"
+    ),
+    prototype = list(
+        k = 0.005,
+        n = 5,
+        omega = 120
+    ),
+    contains = "mortalityTable.period"
+)
+
+setMethod("initialize", "mortalityTable.Weibull", function(.Object, k = 1, n = 1, omega = 120, name = NULL, ...) {
+    if (missing(name) || is.null(name)) {
+        name = paste("Weibull mortality, k=", k, ", n=", n, collapse = "")
+    }
+    ages = 0:omega
+    deathProbs = 1 - exp(-k / (n + 1) * ((ages + 1)^(n + 1) - ages^(n + 1)))
+    callNextMethod(.Object, k = k, n = n, omega = omega, name = name, ages = ages, deathProbs = deathProbs, ...)
+})
+
diff --git a/R/mortalityTable.deMoivre.R b/R/mortalityTable.deMoivre.R
new file mode 100644
index 0000000..7de638e
--- /dev/null
+++ b/R/mortalityTable.deMoivre.R
@@ -0,0 +1,42 @@
+#' @include mortalityTable.period.R
+NULL
+
+#' Class mortalityTable.deMoivre - Mortality table with de Moivre's law
+#'
+#' A period life table with maximum age omega dn the time of death identically
+#' distributed on the interval [0, omega]. The only required slot is the maximum
+#' age \code{omega}, all probabilities are calculated from it.
+#' Optionally, a name and loading can be passed (inherited from
+#' \code{\link{mortalityTable}}).
+#'
+#' @slot omega      Maximum age
+#'
+#' @examples
+#' mm = mortalityTable.deMoivre(100)
+#' plot(mm,
+#'      mortalityTable.deMoivre(90),
+#'      mortalityTable.deMoivre(50))
+#'
+#' @export mortalityTable.deMoivre
+#' @exportClass mortalityTable.deMoivre
+mortalityTable.deMoivre = setClass(
+    "mortalityTable.deMoivre",
+    slots = list(
+        omega = "numeric"
+    ),
+    prototype = list(
+        omega = 100
+    ),
+    contains = "mortalityTable.period"
+)
+
+setMethod("initialize", "mortalityTable.deMoivre", function(.Object, omega = 100, name = NULL, ...) {
+    if (missing(name) || is.null(name)) {
+        name = paste("de Moivre mortality, omega=", omega)
+    }
+    callNextMethod(.Object, omega = omega, name = name, ages = 0:omega, deathProbs = c(1 / (omega - 0:(omega - 1)), 1), ...)
+})
+
+
+
+
diff --git a/man/mortalityTable.MakehamGompertz-class.Rd b/man/mortalityTable.MakehamGompertz-class.Rd
new file mode 100644
index 0000000..31a3b92
--- /dev/null
+++ b/man/mortalityTable.MakehamGompertz-class.Rd
@@ -0,0 +1,38 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/mortalityTable.MakehamGompertz.R
+\docType{class}
+\name{mortalityTable.MakehamGompertz-class}
+\alias{mortalityTable.MakehamGompertz-class}
+\alias{mortalityTable.MakehamGompertz}
+\title{Class mortalityTable.MakehamGompertz - Mortality table with Makeham-Gompertz's law}
+\description{
+A period life table following Makeham and Gompertz's law of a mortality rate
+$\mu$ increasing exponentially with age $x$ ($\mu_{x+t} = A + B c^{(x+t)}$).
+The only required slots are the parameters $A$, $B$ and $c$, all probabilities
+are calculated from them, for technical reasons a maximum age of 120 is
+technically assumed.  Optionally, a name and loading can be passed
+(inherited from \code{\link{mortalityTable}}).
+}
+\section{Slots}{
+
+\describe{
+\item{\code{A}}{Parameter A of the Makeham-Gompertz distribution}
+
+\item{\code{B}}{Parameter B of the Makeham-Gompertz distribution}
+
+\item{\code{c}}{Parameter c of the Makeham-Gompertz distribution}
+
+\item{\code{omega}}{Maximum age (default: 150)}
+}}
+
+\examples{
+# A Gompertz mortality, roughtly approximating the Austrian annuitants 2017
+gmp = mortalityTable.MakehamGompertz(A = 0, B = 0.00001, c = 1.11)
+mortalityTables.load("Austria_Annuities_AVOe2005R")
+plot(gmp, AVOe2005R.male, Period=2017)
+
+# A Makeham-Gompertz mortality, approximating the Austrian annuitants 2017
+mg = mortalityTable.MakehamGompertz(A = 0.0002, B = 0.00001, c = 1.11)
+plot(mg, gmp, AVOe2005R.male, Period=2017)
+
+}
diff --git a/man/mortalityTable.Weibull-class.Rd b/man/mortalityTable.Weibull-class.Rd
new file mode 100644
index 0000000..88ac6ca
--- /dev/null
+++ b/man/mortalityTable.Weibull-class.Rd
@@ -0,0 +1,32 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/mortalityTable.Weibull.R
+\docType{class}
+\name{mortalityTable.Weibull-class}
+\alias{mortalityTable.Weibull-class}
+\alias{mortalityTable.Weibull}
+\title{Class mortalityTable.Weibull - Mortality table with Weibull's law}
+\description{
+A period life table following Weibulls's law of a mortality rate
+$\mu$ increasing as a power of $t$ ($\mu_{x+t} = k * (x+t)^n$).
+The only required slots are the parameters $k>0$ and $n>0$, all probabilities
+are calculated from them, for technical reasons a maximum age of 150 is
+technically assumed.  Optionally, a name and loading can be passed
+(inherited from \code{\link{mortalityTable}}).
+}
+\section{Slots}{
+
+\describe{
+\item{\code{k}}{Parameter k of the Weibull distribution}
+
+\item{\code{n}}{Parameter n of the Weibull distribution}
+
+\item{\code{omega}}{Maximum age (default: 120)}
+}}
+
+\examples{
+# A Weibull mortality
+wbl = mortalityTable.Weibull(k = 0.0000000001, n = 4.8)
+mortalityTables.load("Austria_Annuities_AVOe2005R")
+plot(wbl, AVOe2005R.male, Period=2017, ylim = c(0.00005, 1))
+
+}
diff --git a/man/mortalityTable.deMoivre-class.Rd b/man/mortalityTable.deMoivre-class.Rd
new file mode 100644
index 0000000..060015d
--- /dev/null
+++ b/man/mortalityTable.deMoivre-class.Rd
@@ -0,0 +1,27 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/mortalityTable.deMoivre.R
+\docType{class}
+\name{mortalityTable.deMoivre-class}
+\alias{mortalityTable.deMoivre-class}
+\alias{mortalityTable.deMoivre}
+\title{Class mortalityTable.deMoivre - Mortality table with de Moivre's law}
+\description{
+A period life table with maximum age omega dn the time of death identically
+distributed on the interval [0, omega]. The only required slot is the maximum
+age \code{omega}, all probabilities are calculated from it.
+Optionally, a name and loading can be passed (inherited from
+\code{\link{mortalityTable}}).
+}
+\section{Slots}{
+
+\describe{
+\item{\code{omega}}{Maximum age}
+}}
+
+\examples{
+mm = mortalityTable.deMoivre(100)
+plot(mm,
+     mortalityTable.deMoivre(90),
+     mortalityTable.deMoivre(50))
+
+}
-- 
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