a modern tragedy features ordinary people in tragic situations , all central characters die or destroyed in the end.
so, long day's journey into night best fitted for this tragical definition. there rises stern evidence and sorrow in each character of this family . every one of them is clouded with a marked sadness , disappointment, heoplessness outcome of which is a rigid and thick first-rate frustration and tragedy. whether it is Tyron, Mary , Edmund or Jamie each character is destroyed in the end as a consequences of pasimoniousness, drug-addiction, consumption, debauchery and prostitutary. By going through the story we can go in detail for lenghtening this brief and comprehensive answer.
the dama "long day's journey into night" is modern tragedy because in this all the characters are facing internal conflict. they donot want to understand each other except Eugene. they blame each other for their own faults. they give preference to minor subjects and discuss those matters which lead to hatered like the dicussions of tyrone and jamie. it is modern tragedy because the internal conflicts lead all the characters to feel guilty and so the end is not good.