PostgreSQL 9.5 database showing signs of corruption in logs, though clients work normally
If only pg_statistic is affected, you might get out of this cheap:
Set allow_system_table_mods = on in postgresql.conf and restart PostgreSQL. Then run
TRUNCATE pg_catalog.pg_statistic;
ANALYZE;

Don't forget to reset allow_system_table_mods when you are done.
But you shouldn't ever trust a PostgreSQL database cluster that has had database corruption. Create a new cluster, export the old one with pg_dumpall and import it into the new cluster. Then discard the cluster that had data corruption.
You might want to create the new cluster with --data-checksums so that you get an error message if data change while on disk.
Now you should investigate the possible causes. Upgrade to the latest minor release and test your hardware for problems.