where f (x, y) is the density estim

where f (x, y) is the density estimate at the location (x, y); n is the
number of observations, h is the bandwidth or kernel size, K is the
kernel function, and di is the distance between the location (x, y)
and the location of the ith observation. The effect of placing these
humps or kernels over the points is to create a smooth and continuous
surface. The method is known as KDE because around each
point at which the indicator is observed a circular area (the kernel)
of defined bandwidth is created. This takes the value of the
indicator at that point spread into it according to some appropriate
function. Summing all of these values at all places, including those
at which no incidences of the indicator variable were recorded,
gives a surface of density estimates. Density can be measured by
two methods; simple and kernel. The simple method divides the
entire study area to predetermined number of cells and draws a
circular neighbourhood around each cell to calculate the individual
cell density values, which is the ratio of number of features that fall
within the search area to the size of the area. Radius of the circular
neighbourhood affects the resulting density map. If the radius
is, increased there is a possibility that the circular neighbourhood
would include more feature points which results in a smoother
density surface (Silverman, 1986). The kernel method divides the
entire study area into predetermined number of cells. Rather than
considering a circular neighbourhood around each cell (the simple
method), the kernel method draws a circular neighbourhood
around each feature point (the accident) and then a mathematical
equation is applied that goes from 1 at the position of the feature
point to 0 at the neighbourhood boundary (see Fig. 1). Road