STAR (version 0.3-7)

hgamma: Hazard Functions for Some Common Duration Distributions

Description

Hazard functions for the gamma, weibull, lognormal, inverse Gaussian, log logistic and refractory exponential distributions

Usage

hgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE)
hweibull(x, shape, scale = 1, log = FALSE)
hlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)
hinvgauss(x, mu = 1, sigma2 = 1, boundary = NULL, log = FALSE)
hllogis(x, location = 0, scale = 1, log = FALSE)
hrexp(x, rate = 10, rp = 0.005, log = FALSE)

Arguments

x

vector of quantiles.

shape, scale, rate, sdlog

strictly positive parameters. See corresponding distributions for detail.

mu, sigma2, boundary

parameters associated with the inverse Gaussian distribution.

meanlog

parameter associated with the log normal distribution.

location, rp

parameters of the log logistic and refratory exponential.

log

should the log hazard be returned? FALSE by default.

Value

A vector of hazard rates.

Details

These functions are simply obtained by deviding the density by the survival fucntion.

References

Lindsey, J.K. (2004) Introduction to Applied Statistics: A Modelling Approach. OUP.

Lindsey, J.K. (2004) The Statistical Analysis of Stochastic Processes in Time. CUP.

See Also

dinvgauss, dllogis, drexp

Examples

## Not run: 
# ## use a few plots to compare densities and hazard functions
# 
# ## lognormal
# tSeq <- seq(0.001,0.6,0.001)
# meanlog.true <- -2.4
# sdlog.true <- 0.4
# Yd <- dlnorm(tSeq,meanlog.true,sdlog.true)
# Yh <- hlnorm(tSeq,meanlog.true,sdlog.true)
# max.Yd <- max(Yd)
# max.Yh <- max(Yh)
# Yd <- Yd / max.Yd
# Yh <- Yh / max.Yh
# oldpar <- par(mar=c(5,4,4,4))
# plot(tSeq, Yd, type="n", axes=FALSE, ann=FALSE,
#      xlim=c(0,0.6), ylim=c(0,1))
# axis(2,at=seq(0,1,0.2),labels=round(seq(0,1,0.2)*max.Yd,digits=2))
# mtext("Density (1/s)", side=2, line=3)
# axis(1,at=pretty(c(0,0.6)))
# mtext("Time (s)", side=1, line=3)
# axis(4, at=seq(0,1,0.2), labels=round(seq(0,1,0.2)*max.Yh,digits=2))
# mtext("Hazard (1/s)", side=4, line=3, col=2)
# mtext("Lognormal Density and Hazard Functions", side=3, line=2,cex=1.5)
# lines(tSeq,Yd)
# lines(tSeq,Yh,col=2)
# par(oldpar)
# 
# ## inverse Gaussian
# tSeq <- seq(0.001,0.6,0.001)
# mu.true <- 0.075
# sigma2.true <- 3
# Yd <- dinvgauss(tSeq,mu.true,sigma2.true)
# Yh <- hinvgauss(tSeq,mu.true,sigma2.true)
# max.Yd <- max(Yd)
# max.Yh <- max(Yh)
# Yd <- Yd / max.Yd
# Yh <- Yh / max.Yh
# oldpar <- par(mar=c(5,4,4,4))
# plot(tSeq, Yd, type="n", axes=FALSE, ann=FALSE,
#      xlim=c(0,0.6), ylim=c(0,1))
# axis(2,at=seq(0,1,0.2),labels=round(seq(0,1,0.2)*max.Yd,digits=2))
# mtext("Density (1/s)", side=2, line=3)
# axis(1,at=pretty(c(0,0.6)))
# mtext("Time (s)", side=1, line=3)
# axis(4, at=seq(0,1,0.2), labels=round(seq(0,1,0.2)*max.Yh,digits=2))
# mtext("Hazard (1/s)", side=4, line=3, col=2)
# mtext("Inverse Gaussian Density and Hazard Functions", side=3, line=2,cex=1.5)
# lines(tSeq,Yd)
# lines(tSeq,Yh,col=2)
# par(oldpar)
# 
# ## gamma
# tSeq <- seq(0.001,0.6,0.001)
# shape.true <- 6
# scale.true <- 0.012
# Yd <- dgamma(tSeq, shape=shape.true, scale=scale.true)
# Yh <- hgamma(tSeq, shape=shape.true, scale=scale.true)
# max.Yd <- max(Yd)
# max.Yh <- max(Yh)
# Yd <- Yd / max.Yd
# Yh <- Yh / max.Yh
# oldpar <- par(mar=c(5,4,4,4))
# plot(tSeq, Yd, type="n", axes=FALSE, ann=FALSE,
#      xlim=c(0,0.6), ylim=c(0,1))
# axis(2,at=seq(0,1,0.2),labels=round(seq(0,1,0.2)*max.Yd,digits=2))
# mtext("Density (1/s)", side=2, line=3)
# axis(1,at=pretty(c(0,0.6)))
# mtext("Time (s)", side=1, line=3)
# axis(4, at=seq(0,1,0.2), labels=round(seq(0,1,0.2)*max.Yh,digits=2))
# mtext("Hazard (1/s)", side=4, line=3, col=2)
# mtext("Gamma Density and Hazard Functions", side=3, line=2,cex=1.5)
# lines(tSeq,Yd)
# lines(tSeq,Yh,col=2)
# par(oldpar)
# 
# ## Weibull
# tSeq <- seq(0.001,0.6,0.001)
# shape.true <- 2.5
# scale.true <- 0.085
# Yd <- dweibull(tSeq, shape=shape.true, scale=scale.true)
# Yh <- hweibull(tSeq, shape=shape.true, scale=scale.true)
# max.Yd <- max(Yd)
# max.Yh <- max(Yh)
# Yd <- Yd / max.Yd
# Yh <- Yh / max.Yh
# oldpar <- par(mar=c(5,4,4,4))
# plot(tSeq, Yd, type="n", axes=FALSE, ann=FALSE,
#      xlim=c(0,0.6), ylim=c(0,1))
# axis(2,at=seq(0,1,0.2),labels=round(seq(0,1,0.2)*max.Yd,digits=2))
# mtext("Density (1/s)", side=2, line=3)
# axis(1,at=pretty(c(0,0.6)))
# mtext("Time (s)", side=1, line=3)
# axis(4, at=seq(0,1,0.2), labels=round(seq(0,1,0.2)*max.Yh,digits=2))
# mtext("Hazard (1/s)", side=4, line=3, col=2)
# mtext("Weibull Density and Hazard Functions", side=3, line=2,cex=1.5)
# lines(tSeq,Yd)
# lines(tSeq,Yh,col=2)
# par(oldpar)
# 
# ## refractory exponential
# tSeq <- seq(0.001,0.6,0.001)
# rate.true <- 20
# rp.true <- 0.01
# Yd <- drexp(tSeq, rate.true, rp.true)
# Yh <- hrexp(tSeq, rate.true, rp.true)
# max.Yd <- max(Yd)
# max.Yh <- max(Yh)
# Yd <- Yd / max.Yd
# Yh <- Yh / max.Yh
# oldpar <- par(mar=c(5,4,4,4))
# plot(tSeq, Yd, type="n", axes=FALSE, ann=FALSE,
#      xlim=c(0,0.6), ylim=c(0,1))
# axis(2,at=seq(0,1,0.2),labels=round(seq(0,1,0.2)*max.Yd,digits=2))
# mtext("Density (1/s)", side=2, line=3)
# axis(1,at=pretty(c(0,0.6)))
# mtext("Time (s)", side=1, line=3)
# axis(4, at=seq(0,1,0.2), labels=round(seq(0,1,0.2)*max.Yh,digits=2))
# mtext("Hazard (1/s)", side=4, line=3, col=2)
# mtext("Refractory Exponential Density and Hazard Functions", side=3, line=2,cex=1.5)
# lines(tSeq,Yd)
# lines(tSeq,Yh,col=2)
# par(oldpar)
# 
# ## log logistic
# tSeq <- seq(0.001,0.6,0.001)
# location.true <- -2.7
# scale.true <- 0.025
# Yd <- dllogis(tSeq, location.true, scale.true)
# Yh <- hllogis(tSeq, location.true, scale.true)
# max.Yd <- max(Yd)
# max.Yh <- max(Yh)
# Yd <- Yd / max.Yd
# Yh <- Yh / max.Yh
# oldpar <- par(mar=c(5,4,4,4))
# plot(tSeq, Yd, type="n", axes=FALSE, ann=FALSE,
#      xlim=c(0,0.6), ylim=c(0,1))
# axis(2,at=seq(0,1,0.2),labels=round(seq(0,1,0.2)*max.Yd,digits=2))
# mtext("Density (1/s)", side=2, line=3)
# axis(1,at=pretty(c(0,0.6)))
# mtext("Time (s)", side=1, line=3)
# axis(4, at=seq(0,1,0.2), labels=round(seq(0,1,0.2)*max.Yh,digits=2))
# mtext("Hazard (1/s)", side=4, line=3, col=2)
# mtext("Log Logistic Density and Hazard Functions", side=3, line=2,cex=1.5)
# lines(tSeq,Yd)
# lines(tSeq,Yh,col=2)
# par(oldpar)
# ## End(Not run)