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BruceET
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Numerically calculate Estimating the mean ofpopulation median from a KDE (approximated by 2 vectors)kernel density estimator

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colorlace
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Numerically calculate the mean of a KDE (approximated by 2 vectors)

I have a 1-d kernel density estimate in the form of two vectors:
x_grid is a vector of x-values at which the density function was sampled
density is a vector of corresponding density values (estimated by a kernel density estimate) at each x value in the x_grid.

If I want the median value of this density function ($m$ where $\int_{-\infty}^{m}{f(x) =0.5}$), then I can approximate this by taking the integral (using a numerical technique such as Trapezoidal rule) from $-\infty$ to $x_0, x_1, x_2, ...$ until I get (close enough to) $0.5$.

Essentially, I'm just summing up the areas of trapezoids under the curve until I reach a cumulative sum of $0.5$.

How can I do something similar, but for the mean/expected value of the density function?