A computing device provides distributed estimation of an empirical distribution function. A boundary cumulative distribution function (CDF) value is defined at a start of each region of a plurality of regions. An accuracy value is defined for each region. (a) First equal proportion bins are computed for a first sample of a first marginal variable using the defined boundary CDF value for each region. (b) Second equal proportion bins are computed for the first sample of the first marginal variable within each region based on the defined accuracy value for each region. (c) The computed second equal proportion bins are added as an empirical distribution function (EDF) for the first marginal variable. (d) (a) to (c) are repeated for each remaining sample of the first marginal variable. (e) (a) to (d) are repeated with each remaining marginal variable of a plurality of marginal variables as the first marginal variable.