Email: The empirical distribution function (ecdf) is unbiased in the usual sense, but shows certain order bias. Pyke suggested discrete ecdf using expectations of order statistics. Piecewise constant optimal ecdf saves 200%/N of sample size N. Results are compared with linear interpolation for U(0, 1), which require up to sixfold shorter samples at the same accuracy.
Pastushenko, Vassili F.
"Least Error Sample Distribution Function,"
Journal of Modern Applied Statistical Methods: Vol. 8
, Article 6.
Available at: http://digitalcommons.wayne.edu/jmasm/vol8/iss2/6