How to gather dictionary statistics and fixed-objects statistics

Use the procedures

dbms_stats.gather_dictionary_stats
and
dbms_stats.gather_fixed_objects_stats

Examples:

BEGIN
   DBMS_STATS.GATHER_DICTIONARY_STATS (
     estimate_percent  => DBMS_STATS.AUTO_SAMPLE_SIZE
     ,method_opt        => 'FOR ALL COLUMNS SIZE AUTO'
     ,degree            => NULL
     ,cascade           => DBMS_STATS.AUTO_CASCADE
     ,granularity       => 'AUTO'
     ,no_Invalidate     => DBMS_STATS.AUTO_INVALIDATE);
 END;
 /

 BEGIN
   DBMS_STATS.GATHER_FIXED_OBJECTS_STATS;
 END;
 /

Used in a simple shell script:

#!/usr/bin/ksh
# Gather dictionary and fixed objects stats as recommended by oracle

cat << EoF > ${SCRIPT_BASE}/sql/gather_dict_stats.sql
alter session set nls_date_format='DD-MM-YYYY HH24:MI:SS';
spool ${SCRIPT_BASE}/log/gather_dict_stats.log append
set timing on
select 'Start time: ' || sysdate as "startime" from dual;
execute dbms_stats.gather_dictionary_stats(estimate_percent=>DBMS_STATS.AUTO_SAMPLE_SIZE,method_opt=>'FOR ALL COLUMNS SIZE AUTO',degree=>DBMS_STATS.DEFAULT_DEGREE,granularity=>'ALL',cascade=>DBMS_STATS.AUTO_CASCADE,options=>'GATHER AUTO',no_invalidate=>DBMS_STATS.AUTO_INVALIDATE);
execute dbms_stats.gather_fixed_objects_stats(NULL);
select 'End time: ' || sysdate as "endtime" from dual;
exit
EoF
sqlplus / as sysdba @${SCRIPT_BASE}/sql/gather_dict_stats.sql
rm -r ${SCRIPT_BASE}/sql/gather_dict_stats.sql
exit

Good sources for further reading: Maria Colgan's blog