hgamma: Hazard Functions for Some Common Duration Distributions

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/durationDist.R

Description

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

Usage

1
2
3
4
5
6
7
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.

Details

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

Value

A vector of hazard rates.

Author(s)

Christophe Pouzat christophe.pouzat@gmail.com

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

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
## 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)

STAR documentation built on May 2, 2019, 11:44 a.m.