Getting weirdly small cdf and pdf values for a set of data of 5 members in R

Question

I am doing a Weibull and normal distribution analysis for a set of my data which are :

336256 620316 958846 1007830 1080401

So to avoid putting the whole code here, I refer you directly to the post I followed :

link

The PDF and CDF plots I get are so small and get this form :

Just as info , I put the Weibull distribution results here , to show the values that are small as well :

update :

as per request I put the code to plot pdf here :

my data are as indicated 336256 620316 958846 1007830 1080401

so to reproduce the code, you need to save it as csv and run this code, on your directory. My problem is that I can change and scale the graphs on

xs <- seq(0, 5, len=500)

by changing to :

xs <- seq(10, 1650000, len=5000)

I get :

The problem is when I change the second and third argument , I mean :

1650000 and len=5000 to for example 9650000, len=5000 , the peaks position also displace and don't remain in the same place so it's not only a re scaling the graph.

#-----------------------------------------------------------------------------
# 5. Bootstrapping the pointwise confidence intervals
#-----------------------------------------------------------------------------
library(MASS) 
library(car)

set.seed(123)

rw.small <- c(336256,620316,958846,1007830,1080401)

xs <- seq(0, 5, len=500)


boot.pdf <- sapply(1:1000, function(i) {
  xi <- sample(rw.small, size=length(rw.small), replace=TRUE)

}
)

boot.cdf <- sapply(1:1000, function(i) {
  xi <- sample(rw.small, size=length(rw.small), replace=TRUE)

}
)   

#-----------------------------------------------------------------------------
# Plot PDF
#-----------------------------------------------------------------------------

par(bg="white", las=1, cex=1.2)
plot(xs, boot.pdf[, 1], type="l", col=rgb(.6, .6, .6, .1), ylim=range(boot.pdf),
     xlab="x", ylab="Probability density")
for(i in 2:ncol(boot.pdf)) lines(xs, boot.pdf[, i], col=rgb(.6, .6, .6, .1))

# Add pointwise confidence bands

quants <- apply(boot.pdf, 1, quantile, c(0.025, 0.5, 0.975))
min.point <- apply(boot.pdf, 1, min, na.rm=TRUE)
max.point <- apply(boot.pdf, 1, max, na.rm=TRUE)
lines(xs, quants[1, ], col="red", lwd=1.5, lty=2)
lines(xs, quants[3, ], col="red", lwd=1.5, lty=2)
lines(xs, quants[2, ], col="darkred", lwd=2)
#lines(xs, min.point, col="purple")
#lines(xs, max.point, col="purple")

Answer 1

"the peaks position also displace"

Could you say what the coordinates of the peaks are in the two different cases?

---

I am not sure what you are all doing. The bootstrapping part is very vague (and I doubt it is correct to do it like that) so I took it out. The code below is creating fine graphs (peaks at the same coordinates every time, but of course when you scale the x-axis the position on the screen/plot shifts). Can you look into this and comment/explain again what your question about the graphs is?

library(MASS) 
library(car)

# settings
set.seed(123)
df <- c(336256,620316,958846,1007830,1080401)
xs <- seq(0, 2*10^6, len=500)

# estimation
MLE.est <- suppressWarnings(fitdistr(df, densfun="weibull", lower = 0))  
boot.pdf <- dweibull(xs, shape=as.numeric(MLE.est[[1]][1]), scale=as.numeric(MLE.est[[1]][2]))
boot.cdf <- pweibull(xs, shape=as.numeric(MLE.est[[1]][1]), scale=as.numeric(MLE.est[[1]][2]))

# plotting
layout(matrix(c(1,2),1))

plot(xs, boot.pdf, type="l", col=1, ylim=range(boot.pdf),
     xlab="x", ylab="")
points(df,dweibull(df, shape=as.numeric(MLE.est[[1]][1]), scale=as.numeric(MLE.est[[1]][2])),pch=21,col=1,bg=2)
title("pdf")

plot(xs, boot.cdf, type="l", col=1, ylim=range(boot.cdf),
     xlab="x", ylab="")
points(df,pweibull(df, shape=as.numeric(MLE.est[[1]][1]), scale=as.numeric(MLE.est[[1]][2])),pch=21,col=1,bg=2)
title("cdf")

legend(0.9*10^6,0.12,c("fit","data points"),col=1,lty=c(1,NA),pch=c(NA,21),pt.bg=c(0,2),cex=0.7)

---

Answer 2

The scale of $x$ on your graphs is nowhere near the five observed values (which have a mean value of 800,729.8, a minimum value of 336,256, and maximum of 1,080,401), and therefore you would expect the very small probabilities on your $y$ axis.