1. A computer-program product tangibly embodied in a non-transitory machine-readable storage medium, the computer-program product including instructions operable to cause a first computing device to perform operations including: fit an empirical distribution function to a marginal probability distribution of a variable within a first sample portion of a random sample to derive a first partial marginal probability distribution approximation, wherein the random sample is divided into a plurality of sample portions comprising the first sample portion and a second sample portion, and wherein the plurality of sample portions is distributed among a plurality of computing devices; fit a first portion of a copula function to a multivariate probability distribution of the first sample portion, wherein the copula function is divided into a plurality of portions comprising the first portion of the copula function and a second portion of the copula function; and transmit an indication of a first likelihood contribution of the first sample portion to a coordinating device to cause a second computing device to fit the second portion of the copula function to a multivariate probability distribution of the second sample portion.