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epanechnikov-like_bump_._pdf [2015/04/09 19:08] nikolaj |
epanechnikov-like_bump_._pdf [2015/04/09 19:08] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#55CCEE: context | @#55CCEE: $x_0,d:{\mathbb R}$ | | | @#55CCEE: context | @#55CCEE: $x_0,d:{\mathbb R}$ | | ||
| - | | @#FF9944: definition | @#FF9944: $k:{\mathbb N}\to{\mathbb R}\to{\mathbb R}_{\ge 0}$ | | + | | @#FF9944: definition | @#FF9944: $k_n:{\mathbb N}\to{\mathbb R}\to{\mathbb R}_{\ge 0}$ | |
| | @#FF9944: definition | @#FF9944: $k_n(x):=\begin{cases} \dfrac{1}{2d}\left(1+\dfrac{1}{2n}\right)\left(1-\left(\dfrac{x-x_0}{d}\right)^{2n}\right) &\hspace{.5cm} \mathrm{if}\hspace{.5cm} \left|x\right|\le 1 \\\\ 0 \hspace{.5cm} &\hspace{.5cm} \mathrm{else} \end{cases} $ | | | @#FF9944: definition | @#FF9944: $k_n(x):=\begin{cases} \dfrac{1}{2d}\left(1+\dfrac{1}{2n}\right)\left(1-\left(\dfrac{x-x_0}{d}\right)^{2n}\right) &\hspace{.5cm} \mathrm{if}\hspace{.5cm} \left|x\right|\le 1 \\\\ 0 \hspace{.5cm} &\hspace{.5cm} \mathrm{else} \end{cases} $ | | ||
