A Framework for Various Types of Mortality / Life Tables.

MortalityTables

The goal of MortalityTables is to provide generic base classes and functions to handle all kinds of actuarial actuarial mortality tables (period and cohort life tables). Cohort and static life tables are implemented, observed data can be used, and existing life tables can be blended or extrapolated to derive new tables.

Furthermore, plotting functions are provided for reports and publications.

Installation

You can install the development version of MortalityTables from GitHub with:

# install.packages("devtools")
devtools::install_github("kainhofer/MortalityTables")

About the package

The MortalityTables package provides the mortalityTable base class and some derived classes to handle different types of mortality tables (also called life tables), mainly used for life insurance. Additionally it provides a plot function to compare multiple life tables either directly using the absolute mortalities in log-linear plots or using relative mortalities as percentages of a given reference table.

Types of Life Tables

Provided types of mortality tables are:

• Base class
  Class mortalityTable

• Period life table
  Class mortalityTable.period(ages, deathProbs, ..., baseYear=2000)

  Death probabilities observed / predicted for one observation year; No dependency on the bith year is assumed.

• Cohort life table using age-specific trends
  Class mortalityTable.trendProjection

  Death probabilities of a given base year are projected into the future using age-specific trends $\lambda_x$. The death probability of an $x$-year old in year baseYear + n is calculated as: $$q_x^{(baseYear+n)} = q_x^{(baseYear)} \cdot e^{-n\cdot\lambda_x}$$

  Consequently, the death probabilities for a person born in year YOB can be calculated as $$q_x^{YOB} = q_x^{(base)} \cdot e^{-(YOB+x-baseYear)\cdot \lambda_x}$$

  • Cohort life table approximation using age shift

  Class mortalityTable.ageShift

  Death probabilities for cohort $YOB$ are obtained by using death probabilities for cohort $X$ and modifying the technical age with a birth-year dependent shift: $$q_x^{YOB} = q_{x+shift(YOB)}^{(base)}$$

  • Mixed life table

  Class mortalityTable.mixed

  Arithmetic mean of two life tables with given weights. This approach is often used to generate unisex life tables by mixing male and female mortalities with given weights (e.g. 70:30 or 40:60)

• Cohort life table using age-specific improvement factors
  Class mortalityTable.improvementFactors

  Project base life table using age-specific improvement factors.

• Pension table
  Class pensionTable

  Four states: active, early retirement / invalidity, old-age pension, death (with optional widow)

  All slots describe the corresponding transition probabilities by a

  mortalityTable-derived object.

Loading the MortalityTables package

library("MortalityTables")

Provided Data Sets

The package provides several real-life life tables published by census bureaus and actuarial associations around the world. You can use the function mortalityTables.list to list all available datasets (if no argument is given) or all datasets that match the given pattern (wildcard character is *). You can then use mortalityTables.load to load either one single data set or all datasets that match the pattern.

# list all datasets for Austria
mortalityTables.list("Austria_*")
#>  [1] "Austria_Annuities"                  "Austria_Annuities_AVOe1996R"       
#>  [3] "Austria_Annuities_AVOe2005R"        "Austria_Annuities_EROMF"           
#>  [5] "Austria_Annuities_RR67"             "Austria_Census"                    
#>  [7] "Austria_Endowments_ADSt2426_2Lives" "Austria_PopulationForecast"        
#>  [9] "Austria_PopulationMCMC"             "Austria_PopulationObserved"        
#> [11] "Austria_VUGesamtbestand_2012-16"

# Load the German annuity table DAV 2004-R
mortalityTables.load("Germany_Annuities_DAV2004R")

# Load all Austrian data sets
mortalityTables.load("Austria_*")
#> Lade nötiges Paket: MortalityLaws
#> Warning: Paket 'MortalityLaws' wurde unter R Version 4.2.3 erstellt

Cohort and Period Mortality Data

Cohort mortality vectors (for a given birth year) or period death probabilities (for a given observation year) can be extracted with the functions periodDeathProbabilities() and deathProbabilities():

mortalityTables.load("Austria_Annuities")
deathProbabilities(AVOe2005R.male, YOB = 1977, ages = 35:50)
#>  [1] 0.0006467352 0.0006741228 0.0007202125 0.0007820113 0.0008524437
#>  [6] 0.0009260103 0.0009794564 0.0010272832 0.0010731228 0.0011227093
#> [11] 0.0011784509 0.0012409740 0.0013080864 0.0013817843 0.0014633494
#> [16] 0.0015513107
deathProbabilities(AVOe2005R.male, YOB = 2023, ages = 35:50)
#>  [1] 0.0001941029 0.0002041420 0.0002200821 0.0002411616 0.0002653197
#>  [6] 0.0002909132 0.0003106056 0.0003288675 0.0003468281 0.0003663459
#> [11] 0.0003882554 0.0004128296 0.0004394048 0.0004687102 0.0005012581
#> [16] 0.0005366270

periodDeathProbabilities(AVOe2005R.male, Period = 2023, ages = 35:50)
#>  [1] 0.0004718782 0.0005066172 0.0005573996 0.0006231746 0.0006993210
#>  [6] 0.0007819197 0.0008511112 0.0009184673 0.0009869854 0.0010620137
#> [11] 0.0011462722 0.0012409740 0.0013445246 0.0014595263 0.0015880515
#> [16] 0.0017292761

If the mortality table is a cohort table, the trend is used to calculate the death probabilities for the given cohort or calendar year. If the table is a static life table, the period and cohort life tables will be identical. If the table is an observed table (i.e. observed death probabilities for each age and year), the data is extracted from the matrix’ rows/columns or diagonals. In all cases, the user does not have use different methods for different underlying tables.

Plotting and Comparing Mortality Data

There are two plotting functions using ggplot: plotMortalityTables() and plotMortalityTableComparisons() to plot the absolute and relative mortalities. For absolute mortalities, the q(x) axis employs a log10-scale. The returned plot is a normal ggplot2 object, so all features provided by ggplot2 can be adde to the plots.

mortalityTables.load("Austria_Annuities")
plotMortalityTables(AVOe2005R.male, AVOe2005R.male.unloaded, AVOe1996R.male, EROM.G1950.male, 
                    YOB = 1977, ages = 0:99, legend.position = c(0.5, 0.65))

plotMortalityTableComparisons(AVOe2005R.male, AVOe2005R.male.unloaded, AVOe1996R.male, EROM.G1950.male, 
                              YOB = 1977, ages = 0:99, legend.position = c(0.5, 0.65))

plotMortalityTrend(AVOe2005R.male, AVOe2005R.male.unloaded, AVOe1996R.male, AVOe1996R.male, EROM.G1950.male)

Further information

For further information on how to use the package, see the “Using the MortalityTables Package” vignette.