Random Variables with Moment-Matching Staircase Density Functions

[摘要] This paper proposes techniques for constructing non-parametric computational models describing the distribution of a continuous output variable given input-output data. These models are called Random Predictor Models (RPMs) because the predicted output corresponding to any given input is a random variable. One common example of an RPM is a Gaussian process (GP) model. In contrast to GP models however, we focus on RPMs having a bounded support set and prescribed values for the mean, and the second-, third-, and fourth-order central moments. The proposed RPMs are designed to match moment functions extracted from the data over a range of minimal spread. This paper presents the feasibility conditions that any random variable must meet in order to satisfy the desired constraints. Furthermore, a particular family of such variables, called staircase because their probability density is a piecewise constant function, is proposed. The ability of these variables to describe a wide range of probability density shapes, and their low computational cost enable the efficient generation of possibly skewed and multimodal RPMs over an input-dependent interval.

[发布日期] 2018-07-20

[学科分类] 数值分析

[关键词] RANDOM VARIABLES;PROBABILITY THEORY;MATHEMATICAL MODELS;SKEWNESS;DATA PROCESSING