Affordable Access

Moments of random variables: A systems-theoretic interpretation

Authors
  • Padoan, A
  • Astolfi, A
Publication Date
Feb 01, 2019
Source
Spiral - Imperial College Digital Repository
Keywords
License
Unknown

Abstract

Moments of continuous random variables admitting a probability density function are studied. We show that, under certain assumptions, the moments of a random variable can be characterised in terms of a Sylvester equation and of the steady-state output response of a specific interconnected system. This allows to interpret well-known notions and results of probability theory and statistics in the language of systems theory, including the sum of independent random variables, the notion of mixture distribution and results from renewal theory. The theory developed is based on tools from the center manifold theory, the theory of the steady-state response of nonlinear systems, and the theory of output regulation. Our formalism is illustrated by means of several examples and can be easily adapted to the case of discrete and of multivariate random variables.

Report this publication

Statistics

Seen <100 times