Bivariate Lognormal Distribution for Characterizing Asbestos Fiber Aerosols

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Abstract
The width and length distributions of fiber aerosols were successfully correlated using a lognormal distribution, and the joint distribution could be described by a bivariate lognormal distribution. Means and variances of the length and width for the joint distribution were the same as those for individual marginal distributions, and the correlation between the width and length was between 0.1 and 0.5. Based on the bivariate lognormal distribution, other physical properties of fiber aerosols of the form Q = aWbLc such as aspect ratio, surface area, volume, and aerodynamic diameter were also shown to be lognormally distributed. The mean and variance of In Q can be estimated from parameters in the bivariate analysis. The result shows the usefulness of this analysis in deriving aspect ratio, volume, and aerodynamic diameter from the basic length-width distribution. It also provides a simple way to convert the number concentration to surface area and mass concentration.