The Lowess command creates a function whose values represent the result of the lowess data smoothing algorithm applied to the input data.

This command calls Statistics[Lowess]. See its help page for more examples and a detailed description.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$X≔\mathrm{Sample}\left(\mathrm{Uniform}\left(0\,\mathrm{\pi }\right)\,200\right)$

${\mathrm{\_rtable}}_{36893628610850497588}$

$\mathrm{Yerror}≔\mathrm{Sample}\left(\mathrm{Normal}\left(0\,0.1\right)\,200\right)$

${\mathrm{\_rtable}}_{36893628610756024788}$

$Y≔\mathrm{map}\left(\sin \,X\right)+\mathrm{Yerror}$

${\mathrm{\_rtable}}_{36893628610756012980}$

$L≔\mathrm{CurveFitting}:-\mathrm{Lowess}\left(X\,Y\,\mathrm{fitorder}=1\,\mathrm{bandwidth}=0.3\right)\:$

$P≔\mathrm{ScatterPlot}\left(X\,Y\right)$

$Q≔\mathrm{plot}\left(L\left(x\right)\,x=0..\mathrm{\pi }\right)$

$R≔\mathrm{plots}:-\mathrm{shadebetween}\left(L\left(x\right)\,0\,x=\frac{\mathrm{\pi }}{8}..\frac{3\mathrm{\pi }}{8}\,\mathrm{showboundary}=\mathrm{false}\,\mathrm{positiveonly}\right)$

$\mathrm{plots}:-\mathrm{display}\left(P\,Q\,R\right)$

$\mathrm{int}\left(L\,\frac{\mathrm{\pi }}{8}..\frac{3\mathrm{\pi }}{8}\,\mathrm{numeric}\,\mathrm{\epsilon }=0.01\right)$

$0.538403465288975$

$\mathrm{Optimization}:-\mathrm{Maximize}\left(L\,\mathrm{map}\left(\mathrm{unapply}\,\left\{-x\,x-\mathrm{\pi }\right\}\,x\right)\,\mathrm{optimalitytolerance}=0.001\right)$

$\left[1.00180213049401101\,\left[\begin{array}{c}1.5815245900666368\end{array}\right]\right]$

The CurveFitting[Lowess] command was introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.