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Commit ad064fac authored by Reinhold Kainhofer's avatar Reinhold Kainhofer
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Style fixes in the vignette

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vignettes/using-the-mortalityTables-package.R
+ 24
− 24
View file @ ad064fac
...@@ -21,43 +21,43 @@ mortalityTables.load("Austria_*") ...@@ -21,43 +21,43 @@ mortalityTables.load("Austria_*")
# Log-linear plot comparing some Austrian census tables # Log-linear plot comparing some Austrian census tables
plot(mort.AT.census.1951.male, mort.AT.census.1991.male, plot(mort.AT.census.1951.male, mort.AT.census.1991.male,
mort.AT.census.2001.male, mort.AT.census.2011.male, mort.AT.census.2001.male, mort.AT.census.2011.male,
legend.position=c(1,0)) legend.position = c(1,0))
# Relative death probabilities in percentage of the latest census # Relative death probabilities in percentage of the latest census
plot(mort.AT.census.1951.male, mort.AT.census.1991.male, plot(mort.AT.census.1951.male, mort.AT.census.1991.male,
mort.AT.census.2001.male, mort.AT.census.2001.male,
reference = mort.AT.census.2011.male, legend.position=c(1,0.75), ylim=c(0,4)) reference = mort.AT.census.2011.male, legend.position = c(1,0.75), ylim = c(0,4))
## ------------------------------------------------------------------------ ## ------------------------------------------------------------------------
# Comparison of two Austrian annuity tables for birth year 1977 # Comparison of two Austrian annuity tables for birth year 1977
plot(AVOe1996R.male, AVOe2005R.male, YOB=1977, title="Comparison for YOB=1977") plot(AVOe1996R.male, AVOe2005R.male, YOB = 1977, title = "Comparison for YOB=1977")
# Comparison of two Austrian annuity tables for observation year 2020 # Comparison of two Austrian annuity tables for observation year 2020
plot(AVOe1996R.male, AVOe2005R.male, Period=2020, title="Comparison for observation year 2020") plot(AVOe1996R.male, AVOe2005R.male, Period = 2020, title = "Comparison for observation year 2020")
## ----message=FALSE------------------------------------------------------- ## ----message=FALSE-------------------------------------------------------
mortalityTables.load("Austria_Annuities") mortalityTables.load("Austria_Annuities")
# Get the cohort death probabilities for Austrian Annuitants born in 1977: # Get the cohort death probabilities for Austrian Annuitants born in 1977:
qx.coh1977 = deathProbabilities(AVOe2005R.male, YOB=1977) qx.coh1977 = deathProbabilities(AVOe2005R.male, YOB = 1977)
# Get the period death probabilities for Austrian Annuitants observed in the year 2020: # Get the period death probabilities for Austrian Annuitants observed in the year 2020:
qx.per2020 = periodDeathProbabilities(AVOe2005R.male, Period=2020) qx.per2020 = periodDeathProbabilities(AVOe2005R.male, Period = 2020)
## ------------------------------------------------------------------------ ## ------------------------------------------------------------------------
# Get the cohort death probabilities for Austrian Annuitants born in 1977 as a mortalityTable.period object: # Get the cohort death probabilities for Austrian Annuitants born in 1977 as a mortalityTable.period object:
table.coh1977 = getCohortTable(AVOe2005R.male, YOB=1977) table.coh1977 = getCohortTable(AVOe2005R.male, YOB = 1977)
# Get the period death probabilities for Austrian Annuitants observed in the year 2020: # Get the period death probabilities for Austrian Annuitants observed in the year 2020:
table.per2020 = getPeriodTable(AVOe2005R.male, Period=2020) table.per2020 = getPeriodTable(AVOe2005R.male, Period = 2020)
# Compare those two in a plot: # Compare those two in a plot:
plot(table.coh1977, table.per2020, title="Comparison of cohort 1977 with Period 2020", legend.position=c(1,0)) plot(table.coh1977, table.per2020, title = "Comparison of cohort 1977 with Period 2020", legend.position = c(1,0))
## ------------------------------------------------------------------------ ## ------------------------------------------------------------------------
lt = mortalityTable.period(name="Sample period lifetable", ages=1:99, deathProbs=exp(-(99:1)/10)) lt = mortalityTable.period(name = "Sample period lifetable", ages = 1:99, deathProbs = exp(-(99:1)/10))
plot(lt, title="Simple log-linear period mortality table") plot(lt, title = "Simple log-linear period mortality table")
deathProbabilities(lt) deathProbabilities(lt)
...@@ -80,10 +80,10 @@ atPlus2.damp = mortalityTable.trendProjection( ...@@ -80,10 +80,10 @@ atPlus2.damp = mortalityTable.trendProjection(
# damping function: 2011: full effect, linear reduction until yearly trend=0 in 2111: # damping function: 2011: full effect, linear reduction until yearly trend=0 in 2111:
# 2011: 100%, 2012: 99%, 2013: 98% => For 2013 we have a cumulative trend # 2011: 100%, 2012: 99%, 2013: 98% => For 2013 we have a cumulative trend
# of 297% instead of 300% for three full yearly trends! # of 297% instead of 300% for three full yearly trends!
dampingFunction = function(n) { n - n*(n+1)/2/100 } dampingFunction = function(n) { n - n * (n + 1) / 2 / 100 }
) )
plot(mort.AT.census.2011.male, atPlus2, atPlus2.damp, YOB=2011, legend.position=c(0.8,0.75)) plot(mort.AT.census.2011.male, atPlus2, atPlus2.damp, YOB = 2011, legend.position = c(0.8,0.75))
## ------------------------------------------------------------------------ ## ------------------------------------------------------------------------
atPlus2.damp2 = mortalityTable.trendProjection( atPlus2.damp2 = mortalityTable.trendProjection(
...@@ -97,15 +97,15 @@ atPlus2.damp2 = mortalityTable.trendProjection( ...@@ -97,15 +97,15 @@ atPlus2.damp2 = mortalityTable.trendProjection(
# until 2021 trend 1, from 2031 trend 2, linearly beteen # until 2021 trend 1, from 2031 trend 2, linearly beteen
dampingFunction = function(year) { dampingFunction = function(year) {
if (year <= 2021) 1 if (year <= 2021) 1
else if (year>2031) 14.5/(year-2011) else if (year > 2031) 14.5/(year - 2011)
else 1 - (year-2021)*(year-2021+1)/20/(year-2011) else 1 - (year - 2021)*(year - 2021 + 1) / 20 / (year - 2011)
} }
) )
plot(mort.AT.census.2011.male, atPlus2, atPlus2.damp, atPlus2.damp2, YOB=2011, legend.position=c(0.8,0.75)) plot(mort.AT.census.2011.male, atPlus2, atPlus2.damp, atPlus2.damp2, YOB = 2011, legend.position = c(0.8,0.75))
## ------------------------------------------------------------------------ ## ------------------------------------------------------------------------
baseTableShift = getCohortTable(atPlus2, YOB=2011); baseTableShift = getCohortTable(atPlus2, YOB = 2011);
baseTableShift@name = "Base table of the shift (YOB 2011)" baseTableShift@name = "Base table of the shift (YOB 2011)"
atShifted = mortalityTable.ageShift( atShifted = mortalityTable.ageShift(
...@@ -127,26 +127,26 @@ atShifted = mortalityTable.ageShift( ...@@ -127,26 +127,26 @@ atShifted = mortalityTable.ageShift(
) )
) )
ageShift(atShifted, YOB=2021) ageShift(atShifted, YOB = 2021)
plot(baseTableShift, atPlus2, atShifted, YOB=2021, legend.position=c(0.8,0.75)) plot(baseTableShift, atPlus2, atShifted, YOB = 2021, legend.position = c(0.8,0.75))
## ------------------------------------------------------------------------ ## ------------------------------------------------------------------------
b=AVOe2005R.female b = AVOe2005R.female
b@name = "Modified Copy" b@name = "Modified Copy"
# only b is modified, not the original table # only b is modified, not the original table
b@modification = function(qx) pmax(qx, 0.01) b@modification = function(qx) pmax(qx, 0.01)
plot(AVOe2005R.female, b, YOB=2000) plot(AVOe2005R.female, b, YOB = 2000)
## ------------------------------------------------------------------------ ## ------------------------------------------------------------------------
AVOe2005R.female.sec = setLoading(AVOe2005R.female, loading = 0.1); AVOe2005R.female.sec = setLoading(AVOe2005R.female, loading = 0.1);
# Make sure the modified table has a new name, otherwise plots might break # Make sure the modified table has a new name, otherwise plots might break
AVOe2005R.female.sec@name = "Table with 10% loading" AVOe2005R.female.sec@name = "Table with 10% loading"
plot(AVOe2005R.female, AVOe2005R.female.sec, title="Original and modified table") plot(AVOe2005R.female, AVOe2005R.female.sec, title = "Original and modified table")
## ------------------------------------------------------------------------ ## ------------------------------------------------------------------------
AVOe2005R.female.mod = setModification(AVOe2005R.female, modification=function (qx) pmax(0.03, qx)); AVOe2005R.female.mod = setModification(AVOe2005R.female, modification = function(qx) pmax(0.03, qx));
# Make sure the modified table has a new name, otherwise plots might break # Make sure the modified table has a new name, otherwise plots might break
AVOe2005R.female.mod@name = "Modified table (lower bound of 3%)" AVOe2005R.female.mod@name = "Modified table (lower bound of 3%)"
plot(AVOe2005R.female, AVOe2005R.female.mod, title="Original and modified table") plot(AVOe2005R.female, AVOe2005R.female.mod, title = "Original and modified table")
vignettes/using-the-mortalityTables-package.Rmd
+ 72
− 31
View file @ ad064fac
...@@ -3,7 +3,7 @@ title: "Using the MortalityTables Package" ...@@ -3,7 +3,7 @@ title: "Using the MortalityTables Package"
author: "Reinhold Kainhofer, reinhold@kainhofer.com" author: "Reinhold Kainhofer, reinhold@kainhofer.com"
date: "`r Sys.Date()`" date: "`r Sys.Date()`"
output: output:
rmarkdown::html_vignette: rmarkdown::html_vignette:
toc: true toc: true
toc_depth: 3 toc_depth: 3
fig_width: 7 fig_width: 7
...@@ -14,13 +14,12 @@ vignette: > ...@@ -14,13 +14,12 @@ vignette: >
%\VignetteEncoding{UTF-8} %\VignetteEncoding{UTF-8}
--- ---
```{r echo = FALSE} ```{r echo = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>") knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
``` ```
The MortalityTables package provides the `mortalityTable` base class and The MortalityTables package provides the `mortalityTable` base class and
some derived classes to handle different types of mortality tables (also some derived classes to handle diffferent types of mortality tables (also
called life tables), mainly called life tables), mainly
used for life insurance. Additionally it provides a plot function to compare used for life insurance. Additionally it provides a plot function to compare
multiple life tables either directly using the absolute mortalities in multiple life tables either directly using the absolute mortalities in
...@@ -62,6 +61,10 @@ Provided types of mortality tables are: ...@@ -62,6 +61,10 @@ Provided types of mortality tables are:
* Cohort life table using age-specific improvement factors * Cohort life table using age-specific improvement factors
: Class `mortalityTable.improvementFactors` : Class `mortalityTable.improvementFactors`
: Project base life table using age-specific improvement factors. : Project base life table using age-specific improvement factors.
* Pension tables
: Class `pensionTable`
: Transition probabilities for a four-state pension model (active, invalid,
retirement and death, with a possible widow in the event of death).
## Loading the MortalityTables package ## Loading the MortalityTables package
```{r message=FALSE} ```{r message=FALSE}
...@@ -88,7 +91,7 @@ mortalityTables.list("Austria_*") ...@@ -88,7 +91,7 @@ mortalityTables.list("Austria_*")
mortalityTables.load("Germany_Annuities_DAV2004R") mortalityTables.load("Germany_Annuities_DAV2004R")
# Load all Austrian data sets # Load all Austrian data sets
mortalityTables.load("Austria_*", wildcard=TRUE) mortalityTables.load("Austria_*")
``` ```
...@@ -100,27 +103,31 @@ for demonstration purposes. ...@@ -100,27 +103,31 @@ for demonstration purposes.
### Plotting life tables ### Plotting life tables
The package provides two functions to plot lifetables: The package provides several functions to plot lifetables:
* `plotMortalityTables(table1, table2, ...)` * `plotMortalityTables(table1, table2, ...)`
: A log-linear plot comparing all given life tables. : A log-linear plot comparing all given life tables.
* `plotMortalityTableComparisons(table1, table2, ..., reference=reftable)` * `plotMortalityTableComparisons(table1, table2, ..., reference=reftable)`
: Plot the given life tables as percentages relative to the reference table : Plot the given life tables as percentages relative to the reference table
* `plotMortalityTrend(table1, table2, ..., YOB, Period)`
: Plot the yearly mortality improvement factors (for either the given
observation year `Period` or the birth-year `YOB`)
Both functionalities are also combined into the S3 plot function for the These functionalities are also combined into the S3 plot function for the
mortalityTable class, so you can usually just call plot on the mortality tables. mortalityTable class, so you can usually just call plot on the mortality tables.
If the `reference` argument is given, `plotMortalityTableComparisons` is used, If the `trend = TRUE` argument is given, `plotMortalityTrend` is used,
if the `reference` argument is given, `plotMortalityTableComparisons` is used,
otherwise `plotMortalityTables` is called. otherwise `plotMortalityTables` is called.
```{r} ```{r}
# Log-linear plot comparing some Austrian census tables # Log-linear plot comparing some Austrian census tables
plot(mort.AT.census.1951.male, mort.AT.census.1991.male, plot(mort.AT.census.1951.male, mort.AT.census.1991.male,
mort.AT.census.2001.male, mort.AT.census.2011.male, mort.AT.census.2001.male, mort.AT.census.2011.male,
legend.position=c(1,0)) legend.position = c(1,0))
# Relative death probabilities in percentage of the latest census # Relative death probabilities in percentage of the latest census
plot(mort.AT.census.1951.male, mort.AT.census.1991.male, plot(mort.AT.census.1951.male, mort.AT.census.1991.male,
mort.AT.census.2001.male, mort.AT.census.2001.male,
reference = mort.AT.census.2011.male, legend.position=c(1,0.75), ylim=c(0,4)) reference = mort.AT.census.2011.male, legend.position = c(1,0.75), ylim = c(0,4))
``` ```
For cohort life tables, the plot functions also take either the `YOB` or the For cohort life tables, the plot functions also take either the `YOB` or the
...@@ -129,10 +136,10 @@ birth year or the period death probabilities for the given observation year. ...@@ -129,10 +136,10 @@ birth year or the period death probabilities for the given observation year.
```{r} ```{r}
# Comparison of two Austrian annuity tables for birth year 1977 # Comparison of two Austrian annuity tables for birth year 1977
plot(AVOe1996R.male, AVOe2005R.male, YOB=1977, title="Comparison for YOB=1977") plot(AVOe1996R.male, AVOe2005R.male, YOB = 1977, title = "Comparison for YOB=1977")
# Comparison of two Austrian annuity tables for observation year 2020 # Comparison of two Austrian annuity tables for observation year 2020
plot(AVOe1996R.male, AVOe2005R.male, Period=2020, title="Comparison for observation year 2020") plot(AVOe1996R.male, AVOe2005R.male, Period = 2020, title = "Comparison for observation year 2020")
``` ```
...@@ -147,10 +154,10 @@ To obtain death probabilities from all the different types of tables, there are ...@@ -147,10 +154,10 @@ To obtain death probabilities from all the different types of tables, there are
```{r message=FALSE} ```{r message=FALSE}
mortalityTables.load("Austria_Annuities") mortalityTables.load("Austria_Annuities")
# Get the cohort death probabilities for Austrian Annuitants born in 1977: # Get the cohort death probabilities for Austrian Annuitants born in 1977:
qx.coh1977 = deathProbabilities(AVOe2005R.male, YOB=1977) qx.coh1977 = deathProbabilities(AVOe2005R.male, YOB = 1977)
# Get the period death probabilities for Austrian Annuitants observed in the year 2020: # Get the period death probabilities for Austrian Annuitants observed in the year 2020:
qx.per2020 = periodDeathProbabilities(AVOe2005R.male, Period=2020) qx.per2020 = periodDeathProbabilities(AVOe2005R.male, Period = 2020)
``` ```
These functions return the death probabilities as a simple, numeric R vector. These functions return the death probabilities as a simple, numeric R vector.
...@@ -162,13 +169,13 @@ There are two similar functions that return the death probabilities as a period ...@@ -162,13 +169,13 @@ There are two similar functions that return the death probabilities as a period
```{r} ```{r}
# Get the cohort death probabilities for Austrian Annuitants born in 1977 as a mortalityTable.period object: # Get the cohort death probabilities for Austrian Annuitants born in 1977 as a mortalityTable.period object:
table.coh1977 = getCohortTable(AVOe2005R.male, YOB=1977) table.coh1977 = getCohortTable(AVOe2005R.male, YOB = 1977)
# Get the period death probabilities for Austrian Annuitants observed in the year 2020: # Get the period death probabilities for Austrian Annuitants observed in the year 2020:
table.per2020 = getPeriodTable(AVOe2005R.male, Period=2020) table.per2020 = getPeriodTable(AVOe2005R.male, Period = 2020)
# Compare those two in a plot: # Compare those two in a plot:
plot(table.coh1977, table.per2020, title="Comparison of cohort 1977 with Period 2020", legend.position=c(1,0)) plot(table.coh1977, table.per2020, title = "Comparison of cohort 1977 with Period 2020", legend.position = c(1,0))
``` ```
...@@ -208,8 +215,8 @@ refer to different persons, being of the corresponding ages in the observation ...@@ -208,8 +215,8 @@ refer to different persons, being of the corresponding ages in the observation
year. All that is needed to create a period life table are the death probabilities year. All that is needed to create a period life table are the death probabilities
and the corresponding ages: and the corresponding ages:
```{r} ```{r}
lt = mortalityTable.period(name="Sample period lifetable", ages=1:99, deathProbs=exp(-(99:1)/10)) lt = mortalityTable.period(name = "Sample period lifetable", ages = 1:99, deathProbs = exp(-(99:1)/10))
plot(lt, title="Simple log-linear period mortality table") plot(lt, title = "Simple log-linear period mortality table")
deathProbabilities(lt) deathProbabilities(lt)
``` ```
...@@ -265,10 +272,10 @@ atPlus2.damp = mortalityTable.trendProjection( ...@@ -265,10 +272,10 @@ atPlus2.damp = mortalityTable.trendProjection(
# damping function: 2011: full effect, linear reduction until yearly trend=0 in 2111: # damping function: 2011: full effect, linear reduction until yearly trend=0 in 2111:
# 2011: 100%, 2012: 99%, 2013: 98% => For 2013 we have a cumulative trend # 2011: 100%, 2012: 99%, 2013: 98% => For 2013 we have a cumulative trend
# of 297% instead of 300% for three full yearly trends! # of 297% instead of 300% for three full yearly trends!
dampingFunction = function(n) { n - n*(n+1)/2/100 } dampingFunction = function(n) { n - n * (n + 1) / 2 / 100 }
) )
plot(mort.AT.census.2011.male, atPlus2, atPlus2.damp, YOB=2011, legend.position=c(0.8,0.75)) plot(mort.AT.census.2011.male, atPlus2, atPlus2.damp, YOB = 2011, legend.position = c(0.8,0.75))
``` ```
The other approach is to assume that instead of the initial trend, after some The other approach is to assume that instead of the initial trend, after some
...@@ -292,12 +299,12 @@ atPlus2.damp2 = mortalityTable.trendProjection( ...@@ -292,12 +299,12 @@ atPlus2.damp2 = mortalityTable.trendProjection(
# until 2021 trend 1, from 2031 trend 2, linearly beteen # until 2021 trend 1, from 2031 trend 2, linearly beteen
dampingFunction = function(year) { dampingFunction = function(year) {
if (year <= 2021) 1 if (year <= 2021) 1
else if (year>2031) 14.5/(year-2011) else if (year > 2031) 14.5/(year - 2011)
else 1 - (year-2021)*(year-2021+1)/20/(year-2011) else 1 - (year - 2021)*(year - 2021 + 1) / 20 / (year - 2011)
} }
) )
plot(mort.AT.census.2011.male, atPlus2, atPlus2.damp, atPlus2.damp2, YOB=2011, legend.position=c(0.8,0.75)) plot(mort.AT.census.2011.male, atPlus2, atPlus2.damp, atPlus2.damp2, YOB = 2011, legend.position = c(0.8,0.75))
``` ```
### Cohort life tables with age-shift ### Cohort life tables with age-shift
...@@ -327,7 +334,7 @@ while age-shifting moves the base curve to the right so that it coincides as ...@@ -327,7 +334,7 @@ while age-shifting moves the base curve to the right so that it coincides as
much as possible with the exact (green) line. much as possible with the exact (green) line.
```{r} ```{r}
baseTableShift = getCohortTable(atPlus2, YOB=2011); baseTableShift = getCohortTable(atPlus2, YOB = 2011);
baseTableShift@name = "Base table of the shift (YOB 2011)" baseTableShift@name = "Base table of the shift (YOB 2011)"
atShifted = mortalityTable.ageShift( atShifted = mortalityTable.ageShift(
...@@ -349,9 +356,9 @@ atShifted = mortalityTable.ageShift( ...@@ -349,9 +356,9 @@ atShifted = mortalityTable.ageShift(
) )
) )
ageShift(atShifted, YOB=2021) ageShift(atShifted, YOB = 2021)
plot(baseTableShift, atPlus2, atShifted, YOB=2021, legend.position=c(0.8,0.75)) plot(baseTableShift, atPlus2, atShifted, YOB = 2021, legend.position = c(0.8,0.75))
``` ```
As one can see, for ages above 40 years, the table with 2% yearly trend and the As one can see, for ages above 40 years, the table with 2% yearly trend and the
...@@ -369,11 +376,11 @@ really be used with extreme care! ...@@ -369,11 +376,11 @@ really be used with extreme care!
Life tables are simple pass-by-value S4 objects, so copying works by simple assignment. Life tables are simple pass-by-value S4 objects, so copying works by simple assignment.
```{r} ```{r}
b=AVOe2005R.female b = AVOe2005R.female
b@name = "Modified Copy" b@name = "Modified Copy"
# only b is modified, not the original table # only b is modified, not the original table
b@modification = function(qx) pmax(qx, 0.01) b@modification = function(qx) pmax(qx, 0.01)
plot(AVOe2005R.female, b, YOB=2000) plot(AVOe2005R.female, b, YOB = 2000)
``` ```
### Adding a security loading to the raw probabilities ### Adding a security loading to the raw probabilities
...@@ -388,7 +395,7 @@ adds the given security loading. ...@@ -388,7 +395,7 @@ adds the given security loading.
AVOe2005R.female.sec = setLoading(AVOe2005R.female, loading = 0.1); AVOe2005R.female.sec = setLoading(AVOe2005R.female, loading = 0.1);
# Make sure the modified table has a new name, otherwise plots might break # Make sure the modified table has a new name, otherwise plots might break
AVOe2005R.female.sec@name = "Table with 10% loading" AVOe2005R.female.sec@name = "Table with 10% loading"
plot(AVOe2005R.female, AVOe2005R.female.sec, title="Original and modified table") plot(AVOe2005R.female, AVOe2005R.female.sec, title = "Original and modified table")
``` ```
### Adding a modification to the raw probabilities ### Adding a modification to the raw probabilities
...@@ -399,9 +406,43 @@ classes have a slot `modification` that takes a function that is passed the vect ...@@ -399,9 +406,43 @@ classes have a slot `modification` that takes a function that is passed the vect
of death probabilities. of death probabilities.
```{r} ```{r}
AVOe2005R.female.mod = setModification(AVOe2005R.female, modification=function (qx) pmax(0.03, qx)); AVOe2005R.female.mod = setModification(AVOe2005R.female, modification = function(qx) pmax(0.03, qx));
# Make sure the modified table has a new name, otherwise plots might break # Make sure the modified table has a new name, otherwise plots might break
AVOe2005R.female.mod@name = "Modified table (lower bound of 3%)" AVOe2005R.female.mod@name = "Modified table (lower bound of 3%)"
plot(AVOe2005R.female, AVOe2005R.female.mod, title="Original and modified table") plot(AVOe2005R.female, AVOe2005R.female.mod, title = "Original and modified table")
``` ```
## Pension Tables
Pension tables generalize mortality tables in that the state space is increased
from two states (alive / dead) to four states (active / invalidity or realy
retirement / old age retirement / dead). As a consequence, there is no longer
just one transition probability, but multiple.
Possible states are:
* active: healty, no pension, typically paying some kin of premium
* incapacity: disablity pension (in most cases permanent), not working, early pension
* retirement: old age pension, usually starting with a fixed age
* dead
* Widow/widower pension (if a widow exists at the time of death)
Correspondingly, the `pensionTable` class offers the following slots describing
transition probabilities for the corresponding state transitions (by a
`mortalityTable`-derived object):
* `qxaa`: death probability of actives (active -> dead)
* `ix`: invalidity probability (active -> incapacity)
* `qix`: death probability of invalid (invalid -> dead)
* `rx`: reactivation probability (incapacity -> active)
* `apx`: retirement probability (active -> retirement), typically 1 for a fixed age
* `apx`: retirement probability of invalids (invalid -> retirement), typically 0 or 1 for a fixed age
* `qpx`: death probability of retired (retired -> dead)
* `hx`: probability of a widow at moment of death (dead -> widow), y(x) age differene
* `qxw`: death probability of widows/widowers
* `qgx`: death probability of total group (irrespective of state)
All functions that handle `mortalityTable` object can be used with these slots.
Additionally, the following functions are provided to obtain the set of all
transition probabilities in one data frame:
* `transitionProbabilities(pension_table, YOB)`
* `periodTransitionProbabilities(pension_table, Period)`
vignettes/using-the-mortalityTables-package.html
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− 70
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