other-demographic-functions: Various demographic functions

In lifecontingencies: Financial and Actuarial Mathematics for Life Contingencies

Various demographic functions

Description

Various demographic functions

Usage

Lxt(object, x, t = 1, fxt = 0.5)

Tx(object, x, fxt = 0.5, axOmega = 1 - fxt)

Arguments

object	a lifetable or actuarialtable object
x	age of the subject
t	duration of the calculation
fxt	fraction of the year of age lived by those who die within the year (so that L_x = l_x - fxt\, d_x, matching Lxt). Defaults to 0.5 (uniform distribution of deaths).
axOmega	mean number of years lived in the last, open-ended age interval by those still alive at the last tabulated age \omega (so that L_\omega = axOmega \cdot l_\omega). The default, 1 - fxt, reproduces the historical behaviour of the function (the last interval is closed assuming survivors live on average half a year longer when fxt = 0.5). Published life tables that leave the last interval open set L_\omega = l_\omega / m_\omega: pass axOmega = 1 / mOmega to reproduce them. Only relevant when l_\omega > 0.

Details

Tx il the sum of years lived since age x by the population of the life table, it is the sum of Lx. The function is provided as is, without any warranty regarding the accuracy of calculations. Use at own risk.

Value

A numeric value

Author(s)

Giorgio Alfredo Spedicato.

References

Actuarial Mathematics (Second Edition), 1997, by Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J.

Examples

data(soaLt)
soa08Act=with(soaLt, new("actuarialtable",interest=0.06,
x=x,lx=Ix,name="SOA2008"))
Lxt(soa08Act, 67,10)
#assumes SOA example life table to be load
data(soaLt)
soa08Act=with(soaLt, new("actuarialtable",interest=0.06,x=x,lx=Ix,name="SOA2008"))
Tx(soa08Act, 67)

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