Calculating the overlap of two histograms as percentage

[Al Bothwell]

Is it possible to calculate the overlap of two histogram as a percentage? I am using a user-written package called "hist_overlay". However, any solution will be appreciated. It not specially looking to calculate the percentage using "hist_overlay".

Example code:

 
sysuse auto
ssc install hist_overlay
hist_overlay mpg, over(foreign) fraction width(5) verbose name(hist1,replace

[Nick Cox]

Sorry, but what is the percentage overlap? Does it depend on the histogram shown -- and so is dependent on bin width and origin -- or is it a characteristic of the raw data?

ranksum

has an option to calculate a useful probability (If I recall correctly Rich Goldstein and I lobbied for its inclusion perhaps 25 years ago.)

. sysuse auto, clear 


. ranksum mpg, by(foreign) porder

Two-sample Wilcoxon rank-sum (Mann–Whitney) test

     foreign |      Obs    Rank sum    Expected
-------------+---------------------------------
    Domestic |       52      1688.5        1950
     Foreign |       22      1086.5         825
-------------+---------------------------------
    Combined |       74        2775        2775

Unadjusted variance     7150.00
Adjustment for ties      -36.95
                     ----------
Adjusted variance       7113.05

H0: mpg(foreign==Domestic) = mpg(foreign==Foreign)
         z = -3.101
Prob > |z| = 0.0019
Exact prob = 0.0016

P{mpg(foreign==Domestic) > mpg(foreign==Foreign)} = 0.271

[Rich Goldstein]

I agree with Nick Cox 's recollection (and also point out that I had previously written such a routine published in STB 22 (1994)