Description Usage Arguments Details Value Note Author(s) References See Also Examples
Density function, distribution function and quantile function for the Weibull distribution.
1 2 3 |
x, q |
vector of quantiles |
p |
vector of probabilities |
shape |
shape parameter by default 1 |
scale |
scale parameter by default 1 |
threshold |
threshold parameter by default 0 |
... |
Arguments that can be passed into |
The Weibull distribution with ‘scale’ parameter alpha, ‘shape’ parameter c and ‘threshold’ parameter zeta has density given by
f(x) = (c/alpha) (((x-zeta)/alpha)^(c-1)) exp(-((x-zeta)/alpha)^c)
The cumulative distribution function is given by
F(x) = 1 - exp(-((x-zeta)/alpha)^c)
dweibull3
gives the density, pweibull3
gives the
distribution function and qweibull3
gives the quantile function.
qweibull3
calls uniroot
for each value of the argument ‘p’.
The solution is consequently not exact; the ... can be used to obtain a more accurate
solution if necessary.
Thomas Roth thomas.roth@tu-berlin.de
Etienne Stockhausen stocdarf@mailbox.tu-berlin.de
Johnson, L., Kotz, S., Balakrishnan, N. (1995) Continuous Univariate Distributions-Volume 1, 2nd ed. New York: John Wiley & Sons.
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 | #Simple Example
dweibull3(x=1,scale=1,shape=5,threshold=0)
temp=pweibull3(q=1,scale=1,shape=5,threshold=0)
temp
qweibull3(p=temp,scale=1,shape=5,threshold=0)
#Visualized Example
#prepare screen
#dev.new()
#split.screen(matrix(c(0,0.5,0,1, 0.5,1,0,1),byrow=TRUE,ncol=4))
##generate values
#x=seq(0,3,length=1000)
##plot different density functions
#screen(1)
#plot(x,y=dweibull3(x,threshold=0,shape=0.5,scale=1),col="green",
# xlim=c(0,2.5),ylim=c(0,2.5),type="l",lwd=2,xlab="x",
# ylab="f(x)",main="Density Function of Weibull-Distribution")
#lines(x,y=dweibull3(x,threshold=0,shape=1,scale=1),lwd=2,col="red")
#lines(x,y=dweibull3(x,threshold=0,shape=1.5,scale=2),lwd=2,col="blue")
#lines(x,y=dweibull3(x,threshold=0,shape=5,scale=1),lwd=2,col="orange")
##add legend
#legend("topright",legend=c(expression(paste(alpha, " = 1 ")*
# paste(c, " = 0.5 ")*paste(zeta," = 0")),
# expression(paste(alpha, " = 1 ")*paste(c, " = 1 ")*
# paste(zeta," = 0")),expression(paste(alpha, " = 2 ")*
# paste(c, " = 1.5 ")*paste(zeta," = 0")),
# expression(paste(alpha, " = 1 ")*paste(c, " = 5 ")*
# paste(zeta," = 0"))),col=c("green","red","blue","orange"),
# text.col="black",lwd=2,bty="0",inset=0.04)
#abline(v=0,lty=2,col="grey")
#abline(h=0,lty=2,col="grey")
##plot different distribution functions
#screen(2)
#plot(x,y=pweibull3(x,threshold=0,shape=0.5,scale=1),col="green",
# xlim=c(0,2.5),ylim=c(0,1),type="l",lwd=2,xlab="x",ylab="F(x)",
# main="Cumulative Distribution Function of Weibull-Distribution")
#lines(x,y=pweibull3(x,threshold=0,shape=1,scale=1),lwd=2,col="red")
#lines(x,y=pweibull3(x,threshold=0,shape=1.5,scale=2),lwd=2,col="blue")
#lines(x,y=pweibull3(x,threshold=0,shape=5,scale=1),lwd=2,col="orange")
####add legend
#legend("bottomright",legend=c(expression(paste(alpha, " = 1 ")*
# paste(c, " = 0.5 ")*paste(zeta," = 0")),
# expression(paste(alpha, " = 1 ")*paste(c, " = 1 ")*
# paste(zeta," = 0")),expression(paste(alpha, " = 2 ")*
# paste(c, " = 1.5 ")*paste(zeta," = 0")),
# expression(paste(alpha, " = 1 ")*paste(c, " = 5 ")*
# paste(zeta," = 0"))),col=c("green","red","blue","orange"),
# text.col="black",lwd=2,bty="0",inset=0.04)
#abline(v=0,lty=2,col="grey")
#abline(h=0,lty=2,col="grey")
#close.screen(all=TRUE)
|
Loading required package: Rsolnp
Loading required package: MASS
Attaching package: ‘qualityTools’
The following object is masked from ‘package:stats’:
sigma
[1] 1.839397
[1] 0.6321206
[1] 0.9999999
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.