Use of the log-normal probability density function to analyze membrane pore size distributions: functional forms and discrepancies

The log-normal probability density function has been used extensively in the characterization of membrane pore size distributions and in the theoretical analysis of the effect of these distributions on membrane transport. There has, however, been considerable discrepancy regarding the proper functional form for this probability distribution as well as the proper interpretation of the parameters used to define the distribution. This short communication examines the different forms that have been presented in the literature for the log-normal distribution, properly interprets the parameters that appear in these functions, and provides the appropriate equations required to transform between these different distributions and properly evaluate the appropriate statistical parameters.