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In statistics, a random vector x is classically represented by a probability density function. 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 support of the probability distribution 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 and dealing with nonlinearities is easier. On the other hand, a probability distribution function provides a more accurate information than a set enclosing its support.
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