How To Plot A Lognormal Curve

The lognormal distribution is used in probability for normally distributing the logarithm of a random variable. Variables that can be written as the product of multiple independent random variables can also be distributed in this way. When plotting a lognormal distribution, there are a couple of important aspects that you should not miss; there is a formula that will be useful during this process. Plot by hand on paper or electronically using specialized software.

Step 1

Sort the point values of the random variable to be lognormally distributed from the smallest to the largest.

Step 2

Check to see if all of the values are positive. If they are not, the lognormal distribution plotting cannot be done.

Step 3

Compute the natural logarithm for each of the values in the previous step. This is a vital step, since the definition of lognormal curves involves plotting the logarithmic function of random variables.

Step 4

Compute the empirical cumulative probability of each value using the formula p(n) = (n – 0.5) / N. "N" is the total number of elements, while "n" is used to denote the current point value.

Step 5

Compute the inverse error function for each element. The inverse error function is defined as erf(x) = 2 / sqrt(π) * integral of e^x^2 dt. In this case, "x" will be replaced with 2p-1, for each one of the "p" values computed above.

Step 6

Plot the points with the coordinates (z(pn), ln(xn)), where xn is used to denote the point values from the first step and z(pn) is the output from Step 5.

Step 7

Draw a line to connect the points. This is the final lognormal curve for this distribution.