Description Usage Arguments Details Value Note Author(s) References See Also Examples
Density function, distribution function and quantile function for the Lognormal distribution.
1 2 3 |
x, q |
vector of quantiles |
p |
vector of probabilities |
meanlog, sdlog |
mean and standard deviation of the distribution on the log scale with default values of ‘0’ and ‘1’ respectively. |
threshold |
threshold parameter by default 0 |
... |
Arguments that can be passed into |
The Lognorm distribution with ‘meanlog’ parameter zeta, ‘meansd’ parameter sigma and ‘threshold’ parameter theta has density given by
f(x) = (1/(sqrt(2*pi)*sigma*(x-theta)))
*exp(-(((log((x-theta))-zeta)^2)/(2*(sigma)^2)))
The cumulative distribution function is given by
F(x) = pnorm((log((x-theta))-zeta)/sigma)
dlnorm3
gives the density, plnorm3
gives the
distribution function and qlnorm3
gives the quantile function.
qlnorm3
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 | #Simple Example
dlnorm3(x=2,meanlog=0,sdlog=1/8,threshold=1)
temp=plnorm3(q=2,meanlog=0,sdlog=1/8,threshold=1)
temp
qlnorm3(p=temp,meanlog=0,sdlog=1/8,threshold=1)
#
##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(0,4,length=1000)
##plot different density functions
#screen(1)
#plot(x,y=dlnorm3(x,0,1/8,1),col="green",xlim=c(0,3),type="l",lwd=2,xlab="x",
# ylab="f(x)",main="Density Function of Log-Normal-Distribution")
#lines(x,y=dlnorm3(x,0,0.5,0),lwd=2,col="red")
#lines(x,y=dlnorm3(x,0,1,0),lwd=2,col="blue")
#lines(x,y=dlnorm3(x,1,1/8,0),lwd=2,col="orange")
##add legend
#legend("topleft",legend=c(expression(paste(zeta," = 0 ")*
# paste(sigma, " = 1/8 ")*paste(theta," = 1")),
# expression(paste(zeta," = 0 ")*paste(sigma, " = 0.5 ")*
# paste(theta," = 0")),expression(paste(zeta," = 0 ")*
# paste(sigma, " = 1 ")*paste(theta," = 0")),
# expression(paste(zeta," = 1 ")*paste(sigma, " = 1/8 ")*
# paste(theta," = 0"))),col=c("green","red","blue","orange"),
# text.col="black",lwd=2,bty="o",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=plnorm3(x,0,1/8,1),col="green",xlim=c(0,3),type="l",lwd=2,xlab="x",
# ylab="F(x)",
# main="Cumulative Distribution Function of Log-Normal-Distribution")
#lines(x,y=plnorm3(x,0,0.5,0),lwd=2,col="red")
#lines(x,y=plnorm3(x,0,1,0),lwd=2,col="blue")
#lines(x,y=plnorm3(x,1,1/8,0),lwd=2,col="orange")
##add legend
#legend("topleft",legend=c(expression(paste(zeta," = 0 ")*
# paste(sigma, " = 1/8 ")*paste(theta," = 1")),
# expression(paste(zeta," = 0 ")*paste(sigma, " = 0.5 ")*
# paste(theta," = 0")),expression(paste(zeta," = 0 ")*
# paste(sigma, " = 1 ")*paste(theta," = 0")),
# expression(paste(zeta," = 1 ")*paste(sigma, " = 1/8 ")*
# paste(theta," = 0"))),col=c("green","red","blue","orange"),
# text.col="black",lwd=2,bty="o",inset=0.04)
#abline(v=0,lty=2,col="grey")
#abline(h=0,lty=2,col="grey")
#close.screen(all=TRUE)
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