[Lingtyp] Frequency of front/back, high/mid vowels

[Sebastian Nordhoff]

Dear list members,
do we have any information about the cross-linguistic validity of the 
following hypotheses?

1) front vowels like /i/, /e/ are more frequent than back vowels like 
/u/, /o/

2) high vowels like /i/, /u/  are more frequent than mid vowels like 
/e/, /o/.

3) "corner vowels" /a/, /i/, /u/ are more frequent than anything else.

I am interested in information about types (phonemic inventory) as well 
as tokens (counts in texts).

Best wishes and than you for your time
Sebastian