Другое решение, использующее defaultdict .
from collections import defaultdict
occurrence = defaultdict(int)
for c in word.lower():
occurrence[c] += 1
print(occurrence)
defaultdict(<class 'int'>, {'a': 2, 'b': 1, 'c': 1, 'd': 1})
Или другой без использования импорта.
occurrence = {}
for c in word.lower():
occurrence[c] = occurrence.get(c,0) + 1
print(occurrence)
{'a': 2, 'b': 1, 'c': 1, 'd': 1}