kdensity

The smooth kdensity option generates and plots a kernel density estimate using Gaussian kernels for the distribution from which a set of values was drawn. Values are taken from the first data column, optional weights are taken from the second column. A Gaussian is placed at the location of each point and the sum of all these Gaussians is plotted as a function. To obtain a normalized histogram, each weight should be 1/number-of-points.

Bandwidth: By default gnuplot calculates and uses the bandwidth which would be optimal for normally distributed data values.

     default_bandwidth = sigma * (4/3N) ** (0.2)

This will usually be a very conservative, i.e. broad bandwidth. Alternatively, you can provide an explicit bandwidth.

     plot $DATA smooth kdensity bandwidth <value> with boxes

The bandwidth used in the previous plot is stored in GPVAL_KDENSITY_BANDWIDTH.

Period: For periodic data individual Gaussian components should be treated as repeating at intervals of one period. One example is data measured as a function of angle, where the period is 2pi. Another example is data indexed by day-of-year and measured over multiple years, where the period is 365. In such cases the period should be provided in the plot command:

     plot $ANGULAR_DAT smooth kdensity period 2*pi with lines