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Just a note

  • Red crosses show the locations of 10 randomly-selected observations from a lognormal distribution.
  • The dotted curve is the probability density of that standard normal population, f[y].
  • The green curve shows the result of Gaussian smoothing using the 'plug in' estimate of h.
  • The Gaussian smoothing function for n observations is the mean normal probability density (or cumulative probability) for n observations of variable Y, at location y, given a standard deviation h.
  • Blue and orange curves on the second graph show the results of undersmoothing and oversmoothing.