Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Set estimation
open-in-new
<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, a <a href="/facts/Random_vector/qMfooyVf">random vector</a> x is classically represented by a <a href="/facts/Probability_density_function/zvfybna4">probability density function</a>. In a set-membership approach or set estimation, x is represented by a set X to which x is assumed to belong. This means that the <a href="/facts/Support_(mathematics)/BTuMGbsb">support</a> of the <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> function of x is included inside X. On the one hand, representing random vectors by sets makes it possible to provide fewer assumptions on the random variables (such as <a href="/facts/Independence_(probability_theory)/NUzQtnUL">independence</a>) and dealing with <a href="/facts/Nonlinearity/4aYItALC">nonlinearities</a> is easier. On the other hand, a probability distribution function provides a more accurate information than a set enclosing its support. </p>