Abstract
The bivariate log-normal distribution and the marginal and conditional distributions are introduced for the description of diameter ( D) and length ( L) distributions of airborne man-made mineral fibres (MMMF). Measured fibre sizes fit this distribution well. The accumulated length-diameter distribution has several unique properties regarding characterization of bulk MMMF and dispersed dust as well as of aerodynamic and biological properties of airborne MMMF. This distribution is shown to be the distribution function of a stochastic variable D L defined as the diameter of a fibre drawn from a fibre population with a probability proportional to the fibre length. The distribution of D L is easy to measure and some underlying formulae can be taken directly from stereology. If ( D,L) is bivariate log-normally distributed, then D L is log-normal. The variances of In D L and In D are identical and a simple formula relates the parameters of the distribution of In D L to the parameters of the bivariate log-normal distribution.
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