On the mode of an empirical histogram for sums
Persi W. Diaconis, David A. Freedman · Pacific Journal of Mathematics · 1982
Suppose S n is a sum of independent, identically distributed random variables, which are integer-valued, with span 1, and have finite fourth moment.If n is large, S n is approximately normal.An empirical histogram for k copies of S n will be close to the normal curve provided k > ^Ίrϊlogn.Suppose now that V~n(logn) z <k