{smcl}
{* *! version 1.0.0  23dec2025}{...}

{title:Title}

{p2colset 5 16 17 2}{...}
{p2col:{hi:cvmtest} {hline 2}}Two-sample Cramer-von Mises equality-of-distributions test {p_end}
{p2colreset}{...}


{marker syntax}{...}
{title:Syntax}

{p 8 17 2}
{cmd:cvmtest}
{varname} {ifin} {cmd:,} {opth "by(varlist:groupvar)"}
[{cmd:,} 
{opt r:eps(#)}
{opt seed(#)} 
{opt p:ower(#)}]

{pstd}
{it:{help varlist:groupvar}} must take on
two distinct values. The distribution of {it:varname} for the first value of
{it:groupvar} is compared with that of the second value.



{synoptset 15 tabbed}{...}
{synopthdr}
{synoptline}
{p2coldent:* {opth "by(varlist:groupvar)"}}specify a binary variable that identifies the two groups{p_end}
{synopt :{opt r:eps(#)}}perform # Monte Carlo permutations; default is {opt reps(1000)}{p_end}
{synopt :{opt seed(#)}}set random-number seed to #{p_end}
{synopt :{opt p:ower(#)}}specify the exponent for the CVM statistic; default is {opt power(2)}{p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}* {opt Required}



{title:Description}

{pstd}
{cmd:cvmtest} performs a two-sample Cramer-von Mises (CVM) permutation test 
to assess whether two samples come from the same distribution. The CVM statistic 
measures the integrated squared difference between the empirical cumulative 
distribution functions (ECDFs) of the two samples. The permutation test provides 
an exact p-value by comparing the observed statistic to its distribution under 
random reassignment of group labels.



{title:Options}

{p 6 8 2}
{opth "by(varlist:groupvar)"} is required. It specifies a binary variable
that identifies the two groups.

{p 6 8 2}
{opt r:eps(#)} specifies the number of random permutations for the test; 
the default is {opt reps(1000)}.

{p 6 8 2}    
{opt seed(#)} sets the random-number seed for reproducible results. 

{p 6 8 2}    
{opt p:ower(#)} specifies the exponent for the CVM statistic calculation; 
the default is {opt power(2)}, which gives the standard Cramer-von 
Mises statistic with quadratic weighting. Other values modify sensitivity:
{opt power(1)} linear weighting (less sensitive to large differences),
{opt power(3+)} which is more sensitive to large distributional differences.



{title:Examples}

{pstd}Set-up{p_end}
{phang2}{cmd:. clear}{p_end}
{phang2}{cmd:. set obs 20}{p_end}
{phang2}{cmd:. gen group = cond(_n < 11,1,2)}{p_end}
{phang2}{cmd:. gen x = runiform() in 1/10}{p_end}
{phang2}{cmd:. replace x = runiform() * 1.30 if group==2}{p_end}

{pstd}{opt cvmtest} using defaults{p_end}
{phang2}{cmd:. cvmtest x, by(group)}

{pstd}{opt cvmtest} with specific seed and more permutations{p_end}
{phang2}{cmd:. cvmtest x, by(group) reps(2000) seed(12345)}{p_end}

{pstd}change power to linear weighting{p_end}
{phang2}{cmd:. cvmtest x, by(group) reps(2000) seed(12345) power(1)}{p_end}



{title:Stored results}

{pstd}
{cmd:cvmtest} stores the following in {cmd:r()}:

{synoptset 12 tabbed}{...}
{p2col 5 14 16 2: Scalars}{p_end}
{synopt:{cmd:r(stat)}}observed CVM statistic{p_end}
{synopt:{cmd:r(p)}}permutation p-value{p_end}
{synopt:{cmd:r(reps)}}number of permutations performed{p_end}
{synopt:{cmd:r(power)}}power parameter specified{p_end}
{p2colreset}{...}

{synoptset 12 tabbed}{...}
{p2col 5 14 16 2: Macros}{p_end}
{synopt:{cmd:r(group1)}}name of group 1{p_end}
{synopt:{cmd:r(group2)}}name of group 2{p_end}
{p2colreset}{...}



{title:References}

{phang}
Cramer, H. 1928. 
On the composition of elementary errors.
{it:Scandinavian Actuarial Journal}
11: 13-74.

{phang}    
von Mises, R. 1931. 
{it:Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik}. 
Leipzig: Deuticke.

{phang}
Dwass, M. 1957. 
Modified randomization tests for nonparametric hypotheses. 
{it:Annals of Mathematical Statistics}
28: 181-187.



{title:Citation of {cmd:cvmtest}}

{p 4 8 2}{cmd:cvmtest} is not an official Stata command. It is a free contribution
to the research community, like a paper. Please cite it as such: {p_end}

{p 4 8 2}
Linden A. (2025). CVMTEST: Stata module to perform a two-sample Cramer-von Mises equality-of-distributions test



{title:Author}

{p 4 4 2}
Ariel Linden{break}
President, Linden Consulting Group, LLC{break}
alinden@lindenconsulting.org{break}



{title:Also see}

{p 4 8 2} {helpb ksmirnov}, {helpb ranksum}, {helpb permute}, {helpb adtest} (if installed), {helpb escftest} (if installed), {helpb distcomp} (if installed) {p_end}