Extended Statistics

Starting 11g, you can create statistics for two or more related columns or an expression on a column that are part of a join condition are corrected. 

Extended statistics on multi-column statistics

DECLARE
  exst_name VARCHAR2(30);
BEGIN
  exst_name := DBMS_STATS.CREATE_EXTENDED_STATS('HR','emp',
             '(last_name,department_id)');
END;
/

SELECT SYS.DBMS_STATS.SHOW_EXTENDED_STATS_NAME('hr','emp',
       '(last_name,department_id)') col_group_name
FROM DUAL
/

COL_GROUP_NAME
--------------------------------------------------------------------------------
SYS_STUAV0Z346SKNRSGSE2XA1MM6L

SQL> select dbms_stats.create_extended_stats('hr','emp','(last_name,department_id)') from dual;

DBMS_STATS.CREATE_EXTENDED_STATS('HR','EMP','(LAST_NAME,DEPARTMENT_ID)')
--------------------------------------------------------------------------------
SYS_STUAV0Z346SKNRSGSE2XA1MM6L

Extended statistics on Expression:

SQL> execute dbms_stats.gather_table_stats('HR','EMP', method_opt =>'for all columns size skewonly for columns(lower(last_name)) size skewonly');

To drop extended stats:

SQL> exec dbms_stats.drop_extended_stats('hr','emp','(last_name,department_id)');

Gathering statistics on Column Groups:
Method_opt enables you to gather statistics on column group: 
FOR ALL COLUMNS SIZE AUTO:  optimizer gathers statistics on all existing column groups
FOR COLUMNS:  The column group is automatically created as part of statistics gathering

exec dbms_stats.gather_table_stats('HR','EMP',METHOD_OPT=>'FOR ALL COLUMNS SIZE SKEWONLY FOR COLUMNS (LAST_NAME, DEPARTMENT_ID) SIZE SKEWONLY');

To monitor column groups about multi column or expression statstistics
SQL> select * from user_stat_extensions;

TABLE_NAME EXTENSION_NAME                 EXTENSION    CREATO DRO
---------- ------------------------------ ------------ ------ ---
EMP        SYS_STUAV0Z346SKNRSGSE2XA1MM6L ("LAST_NAME" USER   YES
                                          ,"DEPARTMENT
                                          _ID")

EMP        SYS_STU$OGQI#ACVJROJQ#33ZBENKN (LOWER("LAST USER   YES
                                          _NAME")

SELECT e.EXTENSION col_group, t.NUM_DISTINCT, t.HISTOGRAM
FROM   USER_STAT_EXTENSIONS e, USER_TAB_COL_STATISTICS t
WHERE  e.EXTENSION_NAME=t.COLUMN_NAME
AND    e.TABLE_NAME=t.TABLE_NAME
AND    t.TABLE_NAME='EMP';