With regards to the API,
Why does the GetCallDetailRecords query not include calls that are included in the GetInboundCallingHistory query?
It seems GetInboundCallingHistory contains a lot more inbound calls than GetCallDetailRecords?
Also, is there a way we can identify missed calls from the data?
The only reason why this might happen is because a client called in but dropped it before getting through to an agent. This might happen while the client is still in the IVR, or queue waiting for an agent. The system will add this entry to Inbound calls but not to Call Detail Records as that is extension oriented.
If this is not the case, please feel free to send us an example so we can investigate further for you.