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Goal: To modify a list of rasters using the histogram-equalize stretch-type

What is the appropriate tool to use to change the stretch type of a list of rasters to histogram equalize with arcpy?

Here is how you access the tool from the ArcMap GUI:

enter image description here

Here is my code sans necessary tool which would preform histogram equalization on all of my rasters.

import arcpy, os

inFolder = "pathway to folder containing rasters"

arcpy.env.workspace = inFolder
arcpy.env.overwriteOutput = True
arcpy.env.parallelProcessingFactor = "50%"

rasterList = arcpy.ListRasters("*", "ALL")  # this calls folder in workspace

newlist = [] 
for raster in rasterList:

# Looking for tool which would help with running Histogram Equalize on all rasters.
# Does such a tool even exist?  I am temporarily calling such tool: Name_of_appropriate_tool
# Tools I have tried are listed below along with explanation 

HistEqualized = Name_of_appropriate_tool(raster)

newlist.append(HistEqualized)

print newlist

I have tried

1. ApplySymbologyFromLayer

ApplySymbologyFromLayer_management (in_layer, in_symbology_layer, {symbology_fields}, {update_symbology})

but I cannot use an in_symbology_layer which would apply to all rasters. The required in_symbology_layer parameter changes all rasters uniformly, whereas the histogram equalize feature accessible in ArcMap -which I want- will change (equalize) all rasters according to their min and max value as well as the distribution of values between the min and max value. This is not a uniform change, it is an alteration which is based on each rasters' unique values.

2. ZonalHistogram

ZonalHistogram (in_zone_data, zone_field, in_value_raster, out_table, {out_graph})

but this just outputs a dBASE table. I want to output a histogram equalized raster, not a table.

3. Stretch Function

This seems to just give me the option of gamma. Gamma modifies each raster according to a standardization equation, but this is not the same standardization equation as the "histogram equalized" standardization equation.

Any advice?

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