Two-stage distributed estimation system

A computing device comprising:

• a processor;
• and
• a non-transitory computer-readable medium operably coupled to the processor, the computer-readable medium having computer-readable instructions stored thereon that, when executed by the processor, cause the computing device to
• define a boundary cumulative distribution function (CDF) value at a start of each region of a plurality of regions;
• define an accuracy value for each region of the plurality of regions;
• (a) compute first equal proportion bins for a first sample of a first marginal variable using the defined boundary CDF value for each region;
• (b) compute second equal proportion bins for the first sample of the first marginal variable within each region based on the defined accuracy value for each region;
• (c) add the computed second equal proportion bins to an empirical distribution function (EDF) for the first marginal variable;
• (d) repeat (a) to (c) for each remaining sample of the first marginal variable;
• (e) repeat (a) to (d) with each remaining marginal variable of a plurality of marginal variables as the first marginal variable;
• and
• (f) output the EDF computed for each marginal variable of the plurality of marginal variables.

A method of distributed estimation of an empirical distribution function, the method comprising:

• defining, by a computing device, a boundary cumulative distribution function (CDF) value at a start of each region of a plurality of regions;
• defining, by the computing device, an accuracy value for each region of the plurality of regions;
• (a) computing, by the computing device, first equal proportion bins for a first sample of a first marginal variable using the defined boundary CDF value for each region;
• (b) computing, by the computing device, second equal proportion bins for the first sample of the first marginal variable within each region based on the defined accuracy value for each region;
• (c) adding, by the computing device, the computed second equal proportion bins to an empirical distribution function (EDF) for the first marginal variable;
• (d) repeating, by the computing device, (a) to (c) for each remaining sample of the first marginal variable;
• (e) repeating, by the computing device, (a) to (d) with each remaining marginal variable of a plurality of marginal variables as the first marginal variable;
• and
• (f) outputting, by the computing device, the EDF computed for each marginal variable of the plurality of marginal variables.