In statistics, what is an intuitive way of saying what an $n$-cube is? how do support of distributions come to be defined by an $n$-cube? are $n$-cubes useful in any applications beyond being a descriptor of dimensionality?
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n-cubes are one basis of fractional factorial designs ... – kjetil b halvorsen Sep 14 '20 at 00:27
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A unit 1-cube is the interval $[0,1]$ (or $(0,1)$ if you want an open rather than a closed interval) - i.e. a 1-cube is a line segment.
A unit 2-cube is the square region $[0,1] \times [0,1]$ (ditto, mutatis mutandis)
A unit 3-cube is the cubical volume $[0,1]^3$ (etc)
Hopefully the connection to the support of a distribution is clear, a unit $k$-cube would be the support for any continuous $k$-vector where each component takes values on the unit interval. For example, since you seem to be looking at copulas a lot lately, presumably you'll recognize that the support of a $k$-variate copula is the unit $k$-cube.
Glen_b
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