The lognormal family is parameterized by a location parameter, μ, and a shape parameter, σ. The lognormal pdf and cdf are given as follows, where the logarithm is to the base e:
where α is a scale parameter, and β is a shape parameter. The Weibull distribution reduces to an exponential distribution when β = 1.
An alternative parameterization is commonly used in the literature and in JMP. In the JMP parameterization, σ is the scale parameter and μ is the location parameter. These are related to the α and β parameterization as follows:

Help created on 9/19/2017