HistogramList with logarithmic bins?

Question

HistogramList gives the possibility to bin the elements in a list. Is it possible to have a logarithmic spacing? In an histogram I would do something like:

Histogram[data, "Log"]

I cannot find anything in the documentation...

Answer 1

EDIT

HistogramList[data, "Log", "Probability"]

or for the counts:

HistogramList[data, "Log", "Count"]

ListPlot[Last@%]

Original answer

data = RandomVariate[NormalDistribution[0, 1], 200];
Histogram[data]

Histogram[data, ScalingFunctions -> {"Log", "Log"}]

Histogram[data, {"Log", "Sturges"}]

Answer 2

As you found in the documentation

HistogramList[data, "Log"]

gives you a logarithmic spacing. But if you're going to create a histogram figure, you'll also need to adjust the heights of the histogram bars so that the area sums to 1 or sums to the sample size depending on the objective. Here's an example:

(* Generate some data *)
data = RandomVariate[LogNormalDistribution[0, 0.5], 1000];

(* Histogram based on the log of the data *)
h = HistogramList[Log[data]];

(* Convert back to original units *)
h[[1]] = Exp[h[[1]]];

(* Generate histogram boxes *)
n = Length[data];
logH=Table[{{h[[1,i]],0},{h[[1,i]],(h[[2,i]]/n)/(h[[1,i+1]]-h[[1,i]])},
{h[[1,i+1]],(h[[2,i]]/n)/(h[[1,i+1]]-h[[1,i]])},{h[[1,i+1]],0}},{i, Length[h[[2]]]}];

(* Plot histogram and true density *)
Show[ListLinePlot[logH, PlotStyle -> {{Thin, Black}}],
 Plot[PDF[LogNormalDistribution[0, 0.5], x], {x, 0, 4}]]