pxt: Functions to evaluate survival, death probabilities and...

In lifecontingencies: Financial and Actuarial Mathematics for Life Contingencies

Functions to evaluate survival, death probabilities and deaths.

Description

These functions evaluate raw survival and death probabilities between age x and x+t

Usage

dxt(object, x, t, decrement)
pxt(object, x, t, fractional = "linear", decrement)
qxt(object, x, t, fractional = "linear", decrement)

Arguments

object	A lifetable, actuarialtable or mdt object.
x	Age of life x. (can be a vector for pxt, qxt).
t	Period until which the age shall be evaluated. Default value is 1. (can be a vector for pxt, qxt).
fractional	Assumptions for fractional age. One of "linear", "hyperbolic", "constant force" (can be abbreviated).
decrement	The reason of decrement (only for mdt class objects). Can be either ordinal numbers or the names of decrements; when several are given the probability (or number) of leaving the table because of any of them is returned.

Details

Fractional assumptions are:

• linear: linear interpolation between consecutive ages, i.e. assume uniform distribution.

• constant force of mortality : constant force of mortality, also known as exponential interpolation.

• hyperbolic: Balducci assumption, also known as harmonic interpolation.

Note that fractional="uniform", "exponential", "harmonic" or "Balducci" is also authorized. See references for details.

dxt, pxt and qxt are S4 generics with methods for lifetable (and hence actuarialtable) and mdt objects; other packages can add methods for new table classes.

For mdt objects with a decrement, {}_tq_x^{(j)} = {}_td_x^{(j)} / l_x^{(\tau)} and pxt returns its complement 1 - {}_tq_x^{(j)}; ages must be tabulated integers and fractional t is interpolated linearly (UDD) within the year.

Value

A numeric value representing requested probability.

Warning

The function is provided as is, without any warranty regarding the accuracy of calculations. The author disclaims any liability for eventual losses arising from direct or indirect use of this software.

Note

Function dxt accepts also fractional value of t. Linear interpolation is used in such case. These functions are called by many other functions.

Author(s)

Giorgio A. Spedicato

References

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

See Also

exn, lifetable

Examples

	#dxt example
	data(soa08Act)
	dxt(object=soa08Act, x=90, t=2)
	#qxt example
	qxt(object=soa08Act, x=90, t=2)
	#pxt example
	pxt(object=soa08Act, x=90, t=2, "constant force" )
	#MDT example (Valdez)
	valdezMdt <- new("mdt", name = "ValdezExample", table = 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)))
	qxt(valdezMdt, x = 50, t = 3, decrement = "heart")
	qxt(valdezMdt, x = 50, t = 3, decrement = c("heart", "accidents"))
	pxt(valdezMdt, x = 50, t = 3)

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