pwe {PWEALL}

Piecewise exponential distribution: hazard, cumulative hazard, density, distribution, survival

Description

This will provide the related functions of the specified piecewise exponential distribution.

Usage

pwe(t=seq(0,5,by=0.5),rate=c(0,5,0.8),tchange=c(0,3))

Arguments

t

A vector of time points.

rate

A vector of event rates

tchange

A strictly increasing sequence of time points at which the event rate changes. The first element of tchange must be zero. It must have the same length as rate.

Details

Let \lambda(t)=\sum_{j=1}^m \lambda_j I(t_{j-1}\le t<t_j) be the hazard function, where \lambda_1,\ldots,\lambda_m are the corresponding elements of rate and t_0,\ldots,t_{m-1} are the corresponding elements of tchange, t_m=\infty. The cumulative hazard function

\Lambda(t)=\sum_{j=1}^m \lambda_j(t\wedge t_j-t\wedge t_{j-1}),

the survival function S(t)=\exp\{-\Lambda(t)\}, the distribution function F(t)=1-S(t) and the density function f(t)=\lambda(t)S(t).

Value

hazard

Hazard function

cumhazard

Cumulative hazard function

density

Density function

dist

Distribution function

surv

Survival function

Note

Version 1.0 (7/19/2016)

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

See Also

rpwe,qpwe

Examples

t<-seq(0,3,by=0.1)
rate<-c(0.6,0.3)
tchange<-c(0,1.75)
pwefun<-pwe(t=t,rate=rate,tchange=tchange)
pwefun