{smcl}
{* 22may2006}{...}
{cmd:help mata mm_variance0()}
{hline}

{title:Title}

{pstd}
{bf:mm_variance0() -- Population variance}


{title:Syntax}

{p 8 12 2}
{it:real matrix}{bind:   }
{cmd:mm_variance0(}{it:X}{cmd:,}
{it:w}{cmd:)}

{p 8 12 2}
{it:real matrix}{bind:   }
{cmd:mm_meanvariance0(}{it:X}{cmd:,}
{it:w}{cmd:)}


{p 4 4 2}
where

{p 12 12 2}
{it:X}:  {it:real matrix X} (rows are observations, columns variables)

{p 12 12 2}
{it:w}:  {it:real colvector w}


{title:Description}

{pstd}
{cmd:mm_variance0(}{it:X}{cmd:,} {it:w}{cmd:)}
returns the population variance matrix of {it:X}. {cmd:mm_variance0()}
differs from official Stata's {helpb mf_variance:variance()} (see help
for {helpb mf_mean:mean()}) in that
it divides the deviation cross products by N instead of N-1, where N
is the number of observations. Essentially,

        {cmd:mm_variance0(}{it:X}{cmd:,} {it:w}{cmd:)} = {cmd:variance(}{it:X}{cmd:,} {it:w}{cmd:)} * (N-1)/N

{pstd}
However, {cmd:mm_variance0()} also produces correct results if
N==1.

{pstd}
{cmd:mm_meanvariance0(}{it:X}{cmd:,} {it: w}{cmd:)}
returns {cmd:mean(}{it:X}{cmd:,}{it:w}{cmd:)\mm_variance0(}{it:X}{cmd:,}{it:w}{cmd:)}.

{pstd}
{it:w} specifies the weight.
Specify {it:w} as 1 to obtain unweighted results.
Rows of {it:X} or {it:w} that contain missing values are omitted
from the calculation, which amounts to casewise deletion.


{title:Remarks}

{pstd}
None.


{title:Conformability}

{pstd}
{cmd:mm_variance0(}{it:X}{cmd:,} {it:w}{cmd:)},
{p_end}
		{it:X}:  {it:n x k}
		{it:w}:  {it:n x 1} or {it:1 x 1}
	   {it:result}:  {it:k x k}

{pstd}
{cmd:mm_meanvariance0(}{it:X}{cmd:,} {it:w}{cmd:)},
{p_end}
		{it:X}:  {it:n x k}
		{it:w}:  {it:n x} 1 or 1 {it:x} 1
	   {it:result}:  ({it:k}+1) {it:x} k


{title:Diagnostics}

{pstd}
The functions omit from the calculation rows that contain missing values
unless all rows contain missing values.  Then the returned result contains all
missing values.


{title:Source code}

{pstd}
{help moremata_source##mm_variance0:mm_variance0.mata},
{help moremata_source##mm_meanvariance0:mm_meanvariance0.mata}

{title:Author}

{pstd} Ben Jann, ETH Zurich, jann@soz.gess.ethz.ch


{title:Also see}

{psee}
Online:  help for
{bf:{help mf_mean:[M-5] mean()}},
{bf:{help moremata}}
{p_end}
