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epanechnikov-like_bump_._pdf [2015/04/09 19:09]
nikolaj
epanechnikov-like_bump_._pdf [2015/11/10 17:58]
nikolaj
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 ===== Epanechnikov-like bump . PDF ===== ===== Epanechnikov-like bump . PDF =====
-==== Set ====+==== Function ​====
 | @#55CCEE: context ​    | @#55CCEE: $x_0,​d:​{\mathbb R}$ | | @#55CCEE: context ​    | @#55CCEE: $x_0,​d:​{\mathbb R}$ |
 | @#FF9944: definition ​ | @#FF9944: $k_n:​{\mathbb N}\to{\mathbb R}\to{\mathbb R}_{\ge 0}$ | | @#FF9944: definition ​ | @#FF9944: $k_n:​{\mathbb N}\to{\mathbb R}\to{\mathbb R}_{\ge 0}$ |
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 $\lim_{n\to\infty}k_n$ is the normed $x_0$-centered rectangle of height $\frac{1}{2d}$. $\lim_{n\to\infty}k_n$ is the normed $x_0$-centered rectangle of height $\frac{1}{2d}$.
  
-We can of course linearly combine ​and normalize to gain PDF’s with several such $k$-bumps to obtain new PDF's.+We can of course linearly combine several such $k$-bumps ​and then normalize ​to obtain new PDF's.
  
 == Theorems == == Theorems ==
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