Bandwidth selection for kernel density estimation, using a Weibull kernel Let $\{s_1,\ldots,s_N\}$ be a collection of N samples. 
I have performed the kernel density estimation using the classical form:
$$
\hat{f}(x) = \frac{1}{Nh}\sum_{i=1}^N  K\left(\frac{x-s_i}{h}\right)
$$
where $K\left(\frac{x-s_i}{h}\right)$ is computed as a Weibull kernel, with $k=1$ and $\lambda=1$.
My question is: which is the easiest way to compute the bandwidth $h$? I am using the sample standard deviation, but it seems to be too small, i.e., the computed PDF appears too noisy at the end.
Thanks.

You could probably try to use the "rule-of-thumb" for density estimation based on the sample size and the standard deviation:
$$1.06\sigma n^{-\frac{1}{5}}$$
There are several other methods, which do not depend on the chosen kernell. One popular is the cross-validation. You may check the chapter 5 in Wand and Jones "Kernel smoothing" and references therein.
