# Non-parametric estimation of probability distributions

## Histograms

### Histograms

## Kernels

### Kernel density estimation

### Smoothing kernel estimation

#### Smoothed kernels

We have \(K(x-x_i)\)

We can smooth this to:

\(K_h(x-x_i)=\dfrac{1}{h}K(\dfrac{x-x_i}{h})\)

Where \(h>0\) is the smoothing bandwidth.

\(f(x)=\dfrac{1}{n}\sum_{i=1}^nK_h(x-x_i)\)