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https://www.statlect.com/glossary/support-of-a-random-variable
Support of random vectors and random matrices. The same definition applies to random vectors. If is a random vector, its support is the set of values that it can take. The concept extends in the obvious manner also to random matrices. Synonyms. The support is sometimes also called range. More details
https://math.stackexchange.com/questions/1604895/expectation-on-a-bounded-support
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http://thirdorderscientist.org/homoclinic-orbit/2013/10/24/kernel-density-estimation-for-random-variables-with-bounded-support-mdash-the-transformation-trick
Thus, the support of this random variable lies on \([0, 1]\), and any guess at the density function should also have support on \([0, 1]\). The kernels used with kernel density estimators generally have support on the entire real line, so there's no way to use them 'out of the box' without getting non-meaningful values for parts of your estimator.
https://www.physicsforums.com/threads/show-that-if-x-is-a-bounded-random-variable-then-e-x-exists.570584/
Jan 25, 2012 · Homework Statement Show that if X is a bounded random variable, then E(X) exists. Homework Equations The Attempt at a Solution I am having trouble of finding out where to begin this proof. This is what I got so far: Suppose X is bounded. Then there exists two numbers a and b such that...
https://en.wikipedia.org/wiki/List_of_probability_distributions
The generalized Pareto distribution has a support which is either bounded below only, or bounded both above and below; The Tukey lambda distribution is either supported on the whole real line, or on a bounded interval, depending on what range the value of one of the parameters of the distribution is in. The Wakeby distribution
https://pdfs.semanticscholar.org/d0f5/d25e4dbecc5add721931bf236a4c1a7bdbf7.pdf
As a result, the support of the kernel density estimator may differ from the support of the random variable and the estimator may be non-zero for negative values of random variable. Moreover, this situation may appear when the kernel function has unbounded as well as bounded support. Removing boundary effects can be done in various ways.
https://www.researchgate.net/publication/311235471_Kernel_estimation_of_cumulative_distribution_function_of_a_random_variable_with_bounded_support
In the paper methods of reducing the so-called boundary effects, which appear in the estimation of certain functional characteristics of a random variable with bounded support, are discussed.
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