It is known that the population of Palestine increased greatly between, say, 1880 and 1948. Apart from Jewish immigration there was also considerable Arab immigration (partly related to the economic impetus the Jews immigrants supplied to the land). Are there statistics that say which proportion of the Arabs in Palestine in 1948 came from families that lived there before 1880?
Looks like you're interested in this: http://en.wikipedia.org/wiki/Demographics_of_Palestine#The_question_of_late_Arab_immigration_to_Palestine
The data to answer your question is immigration stats as exact measures of hereditary do not exist. You could always subtract net immigration from population increases to get a upper bound. (You could do some maths and model immigrant pop growth, but this would be hard and would result in spurious accuracy in this case).
The statement: "there was also considerable Arab immigration (partly related to the economic impetus the Jews immigrants supplied to the land)" is questionable. And the link above should help explore whether this statement is indeed true. For instance, people point out the 1931 census of Palestine only shows 2% of Arabs were born abroad at that time, but others think most immigration was unrecorded etc: a few essays worth of disagreement basically. Since it is a Israel/Palestine issue it is well cited, enjoy.