Diameters vary significantly in a tow of commercial Nicalon(TM) fibres, which is one of the most attractive ceramic reinforcements for structural composites. It was found that the strength distribution of Nicalon fibres could not be adequately characterized using either single- or bi-modal Weibull distribution. A recently proposed modified Weibull distribution can account for the effect of varying diameter in the characterization of fibre strength. To verify the validity of the modified Weibull distribution, comprehensive mechanical testing and fractographic studies have been conducted on Nicalon SiC fibres with diameters varying from 8 to 22 mu m. The experimental results have been reported in Part I. Part II of this paper further modifies the derivation of the modified Weibull distribution to yield a relationship which is similar in form, but soundly based on experimental findings. Factors considered in the modified Weibull distribution include the dependence of fracture toughness and flaw density on fibre diameter, both of which may vary with fibre diameter, as reported in Part I. Comparison with experimental data shows that the current modified Weibull distribution works very well, while both single-modal and bi-modal Weibull distributions are inadequate for describing Nicalon fibres with varying diameters.