name of log(n+1) plot

Question

I am trying to plot a distribution of positive integers which contains a lot of variance. I opted to use the log of the y-values but that causes issues due to the inclusion of zeros. I though of plotting log10(n+1), but it seems a bit janky.

Is this solution used more often?
Does it have a name?
Is there a better/more common method?

Why do any transformation at all? In other words, what do you want your transformation to accomplish? — Dave, Aug 25 '22 at 19:05
@Dave Log(0) amounts to minus infinity, which is hard to plot. By making all values at least 1, I assure that the log is always positive without ignoring the zeros outright. — iHnR, Aug 25 '22 at 21:38
@Dave because 10 and 1000 are hard to distinguish while 1 and 3 aren't. I'll probably not use this method as I expect it to cause confusion, but it seemed like an obvious solution so I wondered if it had a name. — iHnR, Aug 25 '22 at 21:42

score 1 · Accepted Answer · answered Sep 04 '22 at 15:02

I'm not aware of a standard name, but it does appear to be fairly common. Programmatically, it's often implemented as log1p ("log of 1 plus").

stats.SE "Plotting 0 in a log scaled axis"
stats.SE "Interpreting log-log regression with log(1+x) as independent variable", asking about regression with log1p
SAS blog "Log transformations: How to handle negative data values?", suggests $\log(1+\epsilon)$

There's also the "symlog" or "log-modulus" functions when you really care about negative values as well:

SAS blog "A log transformation of positive and negative values" puts forward $\operatorname{sgn}(x)\log(1+|x|)$ as "log-modulus" function
SO "What is the origin of Matplotlib's symlog (a.k.a. symmetrical log) scale?"
SO "Logscale plots with zero values in matplotlib", the answer suggests symlog, but a linked duplicate has an answer suggesting log1p

name of log(n+1) plot

1 Answers1