GATHER STATISTICS AFTER SPLITTING A NEW PARTITION

Hi,  I will appreciate your help with this issue:
We have a partitioned table and we need to split the last partition ( named 9999 with high value = maxvalue).

Since all data will be placed in the new 2009 partition, we plan to follow these steps:

- create an auxiliary table.

- exchange 9999 partition with this table including indexes.

- split the partition 9999 into partitions 2009, 9999.

- exchange the auxiliary table with 2009 partition including indexes.

In this scenario, after we complete this work, do you think we must gather statistics for new partitions or also  global statistics in the involved table or it is not necessary?

Thanks in advance,