# MortalityTables

## Author: Reinhold Kainhofer, reinhold@kainhofer.com

R package implementing actuarial mortality tables (period and cohort life tables)

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 λx. The death probability of an x-year old in year `baseYear + n` is calculated as:
qx(baseYear + n) = qx(baseYear) ⋅ en ⋅ λx
Consequently, the death probabilities for a person born in year `YOB` can be calculated as
qxYOB = qx(base) ⋅ e−(YOB + x − baseYear)⋅λx
• 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:
qxYOB = qx + 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.

``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 available data sets
mortalityTables.list()

# list all datasets for Austria
mortalityTables.list("Austria_*")

# Load the German annuity table DAV 2004-R