A qualitative study of probability density visualization techniques in measurements

• PDF estimation techniques revisited from an engineer viewpoint.
• Comparison of the statistical properties of popular PDF estimators.
• Assessment of the PDF characterization through examples with real measured data.
• Practical guidelines for the measurement engineer to visualize the probability content.

Engineers find interpreting plots of a measured physical variable more straightforward than doing a formal statistical analysis. The default choice to display the data behavior is the histogram. The histogram’s performance has proved to be sufficient. However, histograms have a number of limitations including sensitivity to the binwidth and a non-physical roughness. Over the past years, statisticians have developed different techniques to address these problems. These techniques provide a much clearer visualization of the probability density and a more accurate estimation of the statistical properties of the measured data. Despite their increasing use in other fields, these techniques are rarely used in the measurement community. For instance, most measurement instruments provide histograms only. This review article revisits these techniques from an engineer viewpoint to encourage its use. Different examples that include known and unknown densities result in practical guidelines that help the measurement engineer to visualize the probability content.