independentRatesFromMdt: Extract the full Associated Single Decrement Table (ASDT)...

In lifecontingencies: Financial and Actuarial Mathematics for Life Contingencies

Extract the full Associated Single Decrement Table (ASDT) from an mdt object

Description

independentRatesFromMdt returns a matrix of ASDT independent rates q'^{(j)}_x for every combination of age and decrement in the supplied multiple-decrement table.

Usage

independentRatesFromMdt(object, x, t = 1)

Arguments

object	An mdt object.
x	Optional numeric vector of ages to include. Defaults to all ages tabulated in object except the last. Note that this includes the synthetic ages that new("mdt", ...) adds below the lowest age supplied (e.g. ages 0-49 for a table given from age 50), whose decrements are all attributed to the first cause: pass x explicitly to restrict the result to the ages actually supplied.
t	Period (default 1).

Details

The independent rate for decrement j at age x is obtained under the Uniform Distribution of Deaths (UDD) assumption as

q'^{(j)}_x = 1 - \bigl(1 - q^{(\tau)}_x\bigr)^{q^{(j)}_x / q^{(\tau)}_x},

which is the same formula used by qxt.prime.fromMdt for a single age/decrement pair. independentRatesFromMdt is a convenience wrapper that applies this extraction to all ages and all decrements at once, returning the result as a tidy matrix.

Value

A numeric matrix with one row per age and one column per decrement. Row names are the ages, column names the decrement identifiers.

See Also

qxt.prime.fromMdt for a single age/decrement pair, buildMdtFromIndependentRates for the inverse operation.

Examples

valdezDf <- data.frame(
  x = 50:54,
  lx = c(4832555, 4821937, 4810206, 4797185, 4782737),
  heart = c(5168, 5363, 5618, 5929, 6277),
  accidents = c(1157, 1206, 1443, 1679, 2152),
  other = c(4293, 5162, 5960, 6840, 7631))
valdezMdt <- new("mdt", name = "ValdezExample", table = valdezDf)

# ASDT matrix on the ages actually supplied
independentRatesFromMdt(valdezMdt, x = 50:54)

# Subset of ages
independentRatesFromMdt(valdezMdt, x = 50:52)

lifecontingencies documentation built on Oct. 10, 2026, 9:06 a.m.