# Best way to compare distributions with spikes

Following this question, I am interested on the best way to display four distributions with spikes.

Indeed, I have four distributions with circa 75% of elements in it at the maximum value (1). I am searching for a method that is able to display graphically which distribution is more clustered near the maximum value.

I thought about boxplots, but, as you can see in the plot below, it is not easy to decide which one of the second and the fourth boxes has the most quantity of data clustered near the maximum value (to the right).

I thought about violin plots, but, with data with such spikes I cannot understand how the density of the violins are computed, because at least 75% of data has the maximum value.

I tried to use a barplot. But even if you use fine binning near the maximum value, you have always the 75% at top and it is difficult to me to compare these four distributions.

I thought about qqplot between each couple of distributions, but I am unsure if this method can be used to the scope of defining which distribution is better clustered to the maximum.

Is there any other data visualization method to represent this data in such a way that I can decide which of the four distribution is more clustered near the maximum value?

I don't want to use the mean because can be affected by a far outlier. Neither the median because here the median is always the maximum value.

I was thinking about counting how many points are above a certain threshold, but, how to define a good threshold?

Thanks

• Nick Cox gave you pretty good advice on your last question - so I'm unsure what else you expect. For the last chart it would be better to make a set of small multiple histograms instead of dodging(?) the bars as you did here. Commented Jun 10, 2014 at 12:31
• Last time you asked about this, I suggested comparing ECDFs. Your use of the barplot has a number of issues, but a similar plot could be constructed that avoids most of them. Commented Jun 10, 2014 at 13:34
• Sorry @Glen_b I missed the last part of your old comment.. Thanks
– gc5
Commented Jun 10, 2014 at 13:37
• Is there anything wrong with plotting four separate histograms? You seem to be using ggplot2, so this command is your friend.
– Eoin
Commented Jul 1, 2014 at 11:10

## 2 Answers

From the Glen_b's suggestion I decided to use the empirical cumulative distribution function on each distribution.

May I assume that the distribution named Method1 has the distribution more clustered near one than the others?

Thanks

I suggest you to use box-plots but instead of 0-25%, 25-50%, 50-75%, 75-100% you can use a range that you need like: 0-90%, 90-97%, 97-99%, 99-100%, of course if that is for your usage.