Exponential, Weibull, and Lognormal Plots and Fits
The Weibull distribution is the most popular for eventtime data. There are many ways in which different authors parameterize this distribution (as shown in Various Weibull Parameters in Terms of JMP’s alpha and beta). JMP reports two parameterizations, labeled the lambdadelta extreme value parameterization and the Weibull alphabeta parameterization. The alphabeta parameterization is used in the reliability literature. See Nelson (1990). Alpha is interpreted as the quantile at which 63.2% of the units fail. Beta is interpreted as follows: if beta>1, the hazard rate increases with time; if beta<1, the hazard rate decreases with time; and if beta=1, the hazard rate is constant, meaning it is the exponential distribution.
alpha=alpha

beta=beta


eta=alpha

beta=beta


c = alpha

m = beta


eta=alpha

beta=beta


exp(X beta)=alpha

lambda=beta


beta=alpha

alpha=beta


lambda = 1/alpha

p = beta


lambda=log(alpha)

delta=1/beta


mu=log(alpha)

sigma=1/beta

The lognormal distribution is also very popular. This is the distribution where if you take the log of the values, the distribution is normal. If you want to fit data to a normal distribution, you can take the exp() of it and analyze it as lognormal. See Additional Examples of Fitting Parametric Survival in Fit Parametric Survival.
To see additional options for the exponential, Weibull, and lognormal fits, hold down the Shift key, click the red triangle of the ProductLimit Survival Fit menu, and click on the desired fit.
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