New distribution-free plotting position through an approximation to the beta median

Abstract

Even in the modern software, graphical techniques are often utilized to visualize the data and to determine the actual underlying distribution. In this chapter, a new and better distribution-free formula is obtained via an axiomatic approach leading to a new approximation to the median of the Beta distribution. A comparative study, carried out also by using extensive Monte Carlo simulation, shows the advantages of the new solution especially in estimating the median return period and for each considered sample dimension (N = 5, 15, 30, 50).