have the distinction
Verb
Meaning
be distinguished from others of a similar type by virtue of a notable characteristic
Source: WordNetHypernyms
Examples
I think the British have the distinction above all other nations of being able to put new wine into old bottles without bursting them.
The last 60 years have seen collapse of many democracies. For a poor country, it is more difficult to sustain a democracy. From poverty, we have come to being a developing nation. Not only did we survive, we have the distinction of becoming world's largest democracy.
it has the distinction of being the cheapest restaurant in town