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Does anyone know why I can't seem to get a second derivative of this interpolating function f? In this example, h[x] is zero for all x.

data = Join[RandomVariate[NormalDistribution[-3, 1], 100], RandomVariate[NormalDistribution[3, 1], 100]];
f = PDF[SmoothKernelDistribution[data]];
g = f';
h = g';
Plot[{f[x], g[x], h[x]}, {x, -10, 10}, PlotRange -> All]

enter image description here

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    $\begingroup$ You might try KernelMixtureDistribution to avoid the piecewise linear limitation $\endgroup$
    – Andy Ross
    May 2 '15 at 2:01
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If you plot f, f', and f'' over a much smaller range, the answer will be obvious: the interpolation function f is piecewise linear, f' is piecewise constant (i.e., a step function), and f'' is identically zero within each interval.

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  • $\begingroup$ Oops, I backspaced in the window and the message got messed up. $\endgroup$
    – user15994
    May 1 '15 at 21:35

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