Using an appropriate probability grid, plot the cdf (cumulative distribution function)
data. The data will appear as a straight line on the correct grid. Fortunately, there are
two grids that will cover most of the distributions we need, and making additional ones
isn't too complicated.
To make a Normal (or Lognormal) grid notice that the y-axis is in terms of
number of standard deviations, although it's not labeled that way. So the middle of the
graph is at y=0 and that corresponds to cdf, F(x) = 0.5 = 50%. One standard
deviation unit up (or down) is F(x) = 0.8413 (or 0.1587). Two units up (or down) is
0.9772 (or 0.0228). Three units up (down) is 9987 (0.0013). And so on. These values, and
intermediate values chosen for graphing purposes, are tabulated everywhere and can be
found using MS EXCEL also. If the x-axis is to represent a normally distributed x, then
it's Cartesian. If lognormal is what you want, then the x-axis is logarithmic.
To make a grid for the exponential distribution, we can take advantage of
knowing that the exponential distribution is a special case of the Weibull, when the slope
parameter, beta, equals one. The Weibull grid is even easier to make than the Normal grids
because F(x) has a closed form (unlike the Normal), viz.
A little arithmetic shows that
This is a linear equation, Y=M*X+B, where X=ln(x) and Y=ln(-ln(1-F(x))),
with slope of M =