Gathering Fixed Objects Statistics

What are the fixed objects:
Fixed objects are the x$ tables and their indexes.

Why we must gather statistics on fixed objects:
If the statistics are not gathered on fixed objects, the Optimizer will use predefined default values for the statistics. These defaults may lead to inaccurate execution plans.

Does Oracle gather statistics on fixed objects:
Statistics on fixed objects are not being gathered automatically nor within gathering database stats procedure. Starting with 12.1 fixed object statistics will be gathered for the tables that don't have statistics, but still, this will not produce accurate statistics and hence Oracle recommends the DBA do this job himself as he/she knows better the peak time of his/her DB.

When we should gather statistics on fixed objects:
-After a major database or application upgrade.
-After implementing a new module.
-After changing the database configuration. e.g. changing the size of memory pools (sga,pga,..).
-Poor performance/Hang encountered while querying dynamic views e.g. V$ views.
-Features that are heavily dependent on fixed objects by design are performing slow, like RMAN, EM and Grid Control.
-This task should be done only a few times per year.

Notes to consider before starting gathering fixed object statistics: 
-It's recommended to Gather the fixed object statistics during peak hours (while the system is busy) or after the peak hours but the sessions are still connected (even if they idle), to guarantee that the fixed object tables have been populated and the statistics are well representing the DB workload.
-Performance degradation may be experienced during gathering fixed object statistics.
-Having no statistics is better than having a non-representative statistics.

How to gather stats on fixed objects:

First Check the last analyzed date: 
SQL> select OWNER, TABLE_NAME, LAST_ANALYZED from dba_tab_statistics where table_name='X$KGLDP';

OWNER        TABLE_NAME       LAST_ANAL
---------    ------------     ---------
SYS          X$KGLDP         20-MAR-12

Second Export the current fixed stats in a table: (in case you need to revert) 
-- Create a Stats table to hold the statistics:
SQL> exec dbms_stats.create_stat_table('SYS','STATS_TABLE_BKP');

-- Export the current statistics into the Stats table
SQL> exec dbms_stats.export_fixed_objects_stats(stattab=>'STATS_TABLE_BKP',statown=>'SYS'); 

Last Gather fixed objects stats:
SQL> exec dbms_stats.gather_fixed_objects_stats;

Important Note:
Above command will take a while to complete, once it finishes, it's important to flush the shared pool to get an immediate reflection of the new gathered statistics and let the magic happen:
 SQL> ALTER SYSTEM FLUSH SHARED_POOL;
Remember, it's always recommended to run FLUSH SHARED_POOL command during the least workload times on the DB; as it will force the hard parse of most of the queries on the DB, the thing will slow down the applications for some time; till most of the queries get hard parsed again.

In case of reverting to the old statistics:
In case you experienced bad performance on fixed tables after gathering the new statistics you can revert to the old statistics you already backed up:
 SQL> exec dbms_stats.delete_fixed_objects_stats();  
 SQL> exec DBMS_STATS.import_fixed_objects_stats(stattab =>'STATS_TABLE_BKP', STATOWN =>'SYS');


Update on uncovered fixed objects by gather_fixed_objects_stats procedure: [05-01-2020]
Some fixed objects are not covered by gather_fixed_objects_stats procedure like X$KTFBUE which used by views that show segments size; like DBA_EXTENTS and DBA_FREE_SPACE, in case you observe slowness when querying those views then you have to gather the statistics for the underlying fixed table using the following procedure:
SQL> EXEC DBMS_STATS.GATHER_TABLE_STATS ('SYS','X$KTFBUE');
It's recommended to flush the shared pool:
SQL> ALTER SYSTEM FLUSH SHARED_POOL;

In case you still facing slowness after gathering the fixed objects' statistics, it's recommended to purge the RECYCLEBIN as a workaround:
SQL> PURGE DBA_RECYCLEBIN;

 For more reading on Statistics topic:
http://dba-tips.blogspot.com/2012/11/all-about-statistics-in-oracle.html

References:
Oracle white paper: Best Practices for Gathering Optimizer Statistics
http://www.oracle.com/technetwork/database/focus-areas/bi-datawarehousing/twp-bp-optimizer-stats-04042012-1577139.pdf
https://blogs.oracle.com/optimizer/fixed-objects-statistics-and-why-they-are-important 
https://weidongzhou.wordpress.com/2015/03/15/fixed-table-stats-issue-after-gathering-fixed-object-stats/