pxt {lifecontingencies}

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 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 an ordinal number or the name of decrement

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.

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" )
	#add another example for MDT