A Guaranteed Blind and Automatic Probability Density Estimation of Raw Measurements

The use of the histogram to characterize the random component in raw measurements is widely known, applied and applauded. However, its correct use to show the features hidden in the data may require some caution and insight. The most important degree of freedom specified by the user is the binwidth. Although standard rules for binwidth selection exist, they offer no guarantees that the histogram reveals all the desired features. Furthermore, the histogram is a discontinuous representation of the underlying probability density function (pdf) of the data but measured data are usually continuous. Smooth alternatives to the histogram have been developed since the 1970s but still require significant user interaction and insight into the true data probability density. In this paper, we investigate a novel technique that offers a smooth estimate of the pdf without any necessary interaction of the user. The method is fully blind and adaptive such that the best graphical representation of the probability density is ensured.