% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/survival_models.R
\name{survival_models}
\alias{survival_models}
\title{Survival models (Chapter 5): core survival functions + parametric models}
\description{
This file provides actuarial survival-model utilities for Chapter 5.
}
\details{
## Age-at-failure random variable (T0)
- `S0(t, ...)` : survival function  S0(t) = Pr(T0 > t)
- `F0(t, ...)` : CDF              F0(t) = Pr(T0 <= t) = 1 - S0(t)
- `f0(t, ...)` : density          f0(t) = d/dt F0(t)
- `hazard0(t, ...)` : hazard      lambda0(t) = f0(t) / S0(t)
- `cumhaz0(t, ...)` : cum hazard  Lambda0(t) = \eqn{\int_0^t \lambda_0(y) dy}

## Conditional (future lifetime) random variable (Tx), given alive at age x
- `tpx(t, x, ...)` :  \eqn{{}_t p_x = S0(x+t)/S0(x)}
- `tqx(t, x, ...)` :  \eqn{{}_t q_x = 1 - {}_t p_x}
- `fx(t, x, ...)`  :  \eqn{f_x(t) = f0(x+t)/S0(x)}

## Expectations
- `ex_complete(x, ...)` : \eqn{\overset{\circ}{e}_x = \int_0^\infty {}_t p_x\,dt}
- `ex_curtate(x, ...)`  : \eqn{e_x = E[K_x] = \sum_{k\ge 1} {}_k p_x} (truncated sum)

## Models supported
- `"uniform"`     (de Moivre)      parameter: `omega`
- `"exponential"` (constant force) parameter: `lambda`
- `"gompertz"`                  parameters: `B`, `c`
- `"makeham"`                   parameters: `A`, `B`, `c`
- `"weibull"`                   parameters: `shape`, `scale`

All functions are vectorized over `t` (and over `x` where applicable).
}
\keyword{internal}
