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?

Answer 1

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