How can I plot a histogram of a long-tailed data using R?

Question

I have data that is mostly centered in a small range (1-10) but there is a significant number of points (say, 10%) which are in (10-1000). I would like to plot a histogram for this data that will focus on (1-10) but will also show the (10-1000) data. Something like a log-scale for th histogram.

Yes, i know this means not all bins are of equal size

A simple hist(x) gives while hist(x,breaks=c(0,1,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2,3,4,5,7.5,10,15,20,50,100,200,500,1000,10000))) gives

none of which is what I want.

update following the answers here I now produce something that is almost exactly what I want (I went with a continuous plot instead of bar-histogram):

breaks <- c(0,1,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2,4,8)
ggplot(t,aes(x)) + geom_histogram(colour="darkblue", size=1, fill="blue") + scale_x_log10('true size/predicted size', breaks = breaks, labels = breaks)![alt text][3]

the only problem is that I'd like to match between the scale and the actual bars plotted. There two options for doing that : the one is simply use the actual margins of the plotted bars (how?) then get "ugly" x-axis labels like 1.1754,1.2985 etc. The other, which I prefer, is to control the actual bins margins used so they will match the breaks.

Answer 1

Log scale histograms are easier with ggplot than with base graphics. Try something like

library(ggplot2)
dfr <- data.frame(x = rlnorm(100, sdlog = 3))
ggplot(dfr, aes(x)) + geom_histogram() + scale_x_log10()

If you are desperate for base graphics, you need to plot a log-scale histogram without axes, then manually add the axes afterwards.

h <- hist(log10(dfr$x), axes = FALSE) 
Axis(side = 2)
Axis(at = h$breaks, labels = 10^h$breaks, side = 1)

For completeness, the lattice solution would be

library(lattice)
histogram(~x, dfr, scales = list(x = list(log = TRUE)))

---

AN EXPLANATION OF WHY LOG VALUES ARE NEEDED IN THE BASE CASE:

If you plot the data with no log-transformation, then most of the data are clumped into bars at the left.

hist(dfr$x)

The hist function ignores the log argument (because it interferes with the calculation of breaks), so this doesn't work.

hist(dfr$x, log = "y")

Neither does this.

par(xlog = TRUE)
hist(dfr$x)

That means that we need to log transform the data before we draw the plot.

    hist(log10(dfr$x))

Unfortunately, this messes up the axes, which brings us to workaround above.

Answer 2

Using ggplot2 seems like the most easy option. If you want more control over your axes and your breaks, you can do something like the following :

EDIT : new code provided

x <- c(rexp(1000,0.5)+0.5,rexp(100,0.5)*100)

breaks<- c(0,0.1,0.2,0.5,1,2,5,10,20,50,100,200,500,1000,10000)
major <- c(0.1,1,10,100,1000,10000)


H <- hist(log10(x),plot=F)


plot(H$mids,H$counts,type="n",
      xaxt="n",
      xlab="X",ylab="Counts",
      main="Histogram of X",
      bg="lightgrey"
)
abline(v=log10(breaks),col="lightgrey",lty=2)
abline(v=log10(major),col="lightgrey")
abline(h=pretty(H$counts),col="lightgrey")
plot(H,add=T,freq=T,col="blue")
#Position of ticks
at <- log10(breaks)

#Creation X axis
axis(1,at=at,labels=10^at)

This is as close as I can get to the ggplot2. Putting the background grey is not that straightforward, but doable if you define a rectangle with the size of your plot screen and put the background as grey.

Check all the functions I used, and also ?par. It will allow you to build your own graphs. Hope this helps.