Estimation, reference ranges and goodness of fit for the three-parameter log-normal distribution.

The three-parameter log-normal distribution (3PL) is an appropriate model for many of the continuous variables encountered in medicine. It is shown how to obtain different types of estimate and approximate (sometimes conservative) confidence intervals for the parameters of the 3PL and for certain functions of them, particularly in the calculation of reference ranges of clinical measurements. A simple non-iterative estimate of the shift parameter is described. The Shapiro-Wilk test of non-normality is modified to allow it to be used for testing for departure from the 3PL. Its power is compared with that of other well-known tests. The methods are illustrated using several data sets.