# pxt: Functions to evaluate survival, death probabilities and... In spedygiorgio/lifecontingencies: Financial and Actuarial Mathematics for Life Contingencies

## Description

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

## Usage

 ```1 2 3``` ```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.

`exn`, `lifetable`
 ```1 2 3 4 5 6 7 8``` ``` #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 ```