On interpreting and extracting information from the cumulative distribution function curve: a new perspective with applications

For any density function (or probability function), there always corresponds a "cumulative distribution function" (cdf). It is a well-known mathematical fact that the cdf is more general than the density function, in the sense that for a given distribution the former may exist without the existence of the latter. Nevertheless, while the density function curve is frequently adopted as a graphical device in depicting the main attributes of the distribution it represents, the cdf curve is usually ignored in such practical analysis. Can the cdf curve be more fruitfully utilised as a graphical device? In this paper, the authors show that the region above a cdf curve can be interpreted as an aggregate value of the underlying random variable. This perspective would facilitate the graphical display of the information contained in the distribution. They also exploit this approach to give intuition to the derivation of some well-known results.