Gaussian Kernel

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.