Graphical presentation of the relationship between values x and cumulative distribution function F(x) in arithmetic scale is not usually suitable when extreme values are of interest. The probabilities of extreme values are relatively small, and it is very hard to read them from such a plot.
A special type of graph used for presenting the relationship between the probability and data values is known as the probability plot. Probability plots are designed for particular theoretical distributions by transforming the scale of the probability axis so that a given distribution is represented by a straight line. This is achieved by introducing so called reduced variable y, which is a transform of F(x) and is linearly related to x.
Usually, horizontal axis of the probability plot shows reduced variable in linear scale and it is accompanied with another horizontal axis showing non-exceedance probability F(x) or exceedance probability 1 – F(x) in non-linear scale. Values x of the random variable are usually plotted on vertical axis. Specially designed graph paper which is ruled with vertical grid for probabilities and horizontal grid for data values is called probability paper.
