We know it from comments in system procedure's code. Here is what I've found while digging for some undocumented stuff about statistics:

-- I don't like this copy&paste stuff, but here it boosts performance by 50%

You can find it too - in sys.sp_table_statistics2_rowset procedure. It returns first 2 parts of DBCC SHOW_STATISTICS result (stat header and density vector) in table format. The procedure header is:

EXEC sys.sp_table_statistics2_rowset
    @table_name = ?, --  sysname
    @table_schema = ?, --  sysname
    @table_catalog = ?, --  sysname
    @stat_name = ?, --  sysname
    @stat_schema = ?, --  sysname
    @stat_catalog = ? --  sysname

If you supply only @table_name and @stat_name, you'll receive the same output as from undocumented (I think) syntax of DBCC SHOW_STATISTICS:

DBCC SHOW_STATISTICS(@table_name, @stat_name) WITH STAT_HEADER JOIN DENSITY_VECTOR