Currently the histogram treats -Infinity and +Infinity as regular values that can be counted, thus allowing them to be bounds in histogram bucket other than the ending values. i.e., there can be a histogram with bucket boundaries:
-inf, -inf, 1, 2, 3, +inf
The first -inf is assigned implicitly by the histogram implementation, the second -inf is added as the first available value.
In this SERVER-99024 we allowed the estimation for -Infinity and allowed as valid bucket the bucket (-inf, -inf].

This ticket suggests counting infinity values separately as done with type counts in this and disregard the Infinity values in the creation of the histogram buckets (prospectively here), while adding their count to the TypeCounts and in the corresponding estimation counts. ($lt, $gt, $ne).