It has been found that for continuous distribution (x,y) the operation z=invcum(y)/(x_max-x_min) gives (x,z) aligned in a straight line. For the discrete quantities it is possible to consider z=invcum(y) or y=cum(x), but the parameters have to be determined by the observed values. The closer the cum(x) is to the original cumulative plot, the cleaner the adjusted plot is.

The figure is the cumulative plot and adjusted plot y=cum(x) obtained for 100 random data generated by the Box-Muller method with σ=1 and av=5. The parameters for the adjustment were determined as follows; a is the average of data, σ the standard deviation of the data, and x_max and x_min determined by the range of data. Note that cum(x) curve is asymmetric with respect to 50%.

If the inverse of cum(x) of the above is applied, the graph is obtained as shown below.

If one chooses a=(x_min+x_max)/2, the graph is obtained as shown below.