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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.
In JMP, the Weibull parameterization defines σ as the scale parameter and μ as the location parameter. These are related to the α and β Weibull parameterization as follows:

Help created on 3/19/2020