Beyond Q-Q plots: Some new graphical tools for the assessment of distributional assumptions and the tail behavior of the data

We introduce some new approaches for the graphical assessment of distribution of the data that supplement the existing graphical methods. Analogous to Q-Q plots and P-P plots, we introduce plots based on arc length and area of surface of revolution of the density function. Thus, our method indirectly makes use not only of density assumed but also of the derivatives thereof. We illustrate, by using several examples, that these plots help us identify the correct distribution and also rule out the incorrect possibilities. We further consider the problem of assessing the behavior of the data toward the tail and develop graphical tools to identify the closest potential probability distribution for the tail. Examples based on real data are provided.