Is it rare to be 19 and have four generations in the family still alive?

Well if a lot of the children in the earlier generations were had at young ages then you could have a new generation once every 16 years (legally) by 80, you can have 4 generations below you, each 16 years younger than the rest. So no, this is not that rare. The human life expectancy has increased so therefore people can live to see their children's children's children.