In general, kernel density estimation is a nonparametric method of estimating
the univariate probability density function of a random variable. The
Gaussian kernel provides a smoothed fit of the data, which enables you
to view the structure of the data without having to impose an artificial
parametric statistical distribution onto the data. As with other smoothing
methods, the amount of smoothing can be controlled through the bandwidth
parameter. In general, the density estimate is smoother for larger values
of the bandwidth and less smooth for smaller values, which correspond
to a more local representation of the density function.

Specifically, at each point the density is estimated as a weighted average according to the following formula:

where Φ is the standard normal density, n is the number of observations, and h is the bandwidth.