fGTDL {GTDL} | R Documentation |
The GTDL distribution
Description
Density function, survival function, failure function and random generation for the GTDL distribution.
Usage
dGTDL(t, param, log = FALSE)
hGTDL(t, param)
sGTDL(t, param)
rGTDL(n, param)
Arguments
t |
vector of integer positive quantile. |
param |
parameters (alpha and gamma are scalars, lambda non-negative). |
log |
logical; if TRUE, probabilities p are given as log(p). |
n |
number of observations. |
Details
Density function
f(t\mid \boldsymbol{\theta})=\lambda\left(\frac{\exp\{\alpha{t}+\boldsymbol{X}^{\top}\boldsymbol{\beta}\}}{1+\exp\{\alpha{t}+\boldsymbol{X}^{\top}\boldsymbol{\beta}\}}\right)\times\left(\frac{1+\exp\{\alpha{t}+\boldsymbol{X}^{\top}\boldsymbol{\beta}\}}{1+\exp\{\boldsymbol{X}^{\top}\boldsymbol{\beta}\}}\right)^{-\lambda/\alpha}
Survival function
S(t \mid \boldsymbol{\theta})=\left(\frac{1+\exp\{\alpha{t}+\boldsymbol{X}^{\top}\boldsymbol{\beta}\}}{1+\exp\{\boldsymbol{X}^{\top}\boldsymbol{\beta}\}}\right)^{-\lambda/\alpha}
Failure function
h(t\mid\boldsymbol{\theta})=\lambda\left(\frac{\exp\{\alpha{t}+\boldsymbol{X}^{\top}\boldsymbol{\beta}\}}{1+\exp\{\alpha{t}+\boldsymbol{X}^{\top}\boldsymbol{\beta}\}}\right)
Value
dGTDL
gives the density function, hGTDL
gives the failure function, sGTDL
gives the survival function and rGTDL
generates random samples.
Invalid arguments will return an error message.
Source
[d-p-q-r]GTDL are calculated directly from the definitions.
References
Mackenzie, G. (1996). Regression Models for Survival Data: The Generalized Time-Dependent Logistic Family. Journal of the Royal Statistical Society. Series D (The Statistician). 45. 21-34.
Examples
library(GTDL)
t <- seq(0,20,by = 0.1)
lambda <- 1.00
alpha <- -0.05
gamma <- -1.00
param <- c(lambda,alpha,gamma)
y1 <- hGTDL(t,param)
y2 <- sGTDL(t,param)
y3 <- dGTDL(t,param,log = FALSE)
tt <- as.matrix(cbind(t,t,t))
yy <- as.matrix(cbind(y1,y2,y3))
matplot(tt,yy,type="l",xlab="time",ylab="",lty = 1:3,col=1:3,lwd=2)
y1 <- hGTDL(t,c(1,0.5,-1.0))
y2 <- hGTDL(t,c(1,0.25,-1.0))
y3 <- hGTDL(t,c(1,-0.25,1.0))
y4 <- hGTDL(t,c(1,-0.50,1.0))
y5 <- hGTDL(t,c(1,-0.06,-1.6))
tt <- as.matrix(cbind(t,t,t,t,t))
yy <- as.matrix(cbind(y1,y2,y3,y4,y5))
matplot(tt,yy,type="l",xlab="time",ylab="Hazard function",lty = 1:3,col=1:3,lwd=2)