Loss Distribution Calculation Using Discrete Bounds

The patent segments the loss distribution calculation into multiple discrete components: frequency distribution calculation, scale distribution discretization, and composite distribution assembly. By dividing the continuous loss distribution into discrete bins and calculating contributions from each bin separately, the method achieves deterministic results while maintaining computational tractability. This segmentation eliminates random number generation while preserving the essential stochastic characteristics through discrete probability mass functions.

The patent transforms the continuous scale distribution parameters into discrete parameters through discretization. By converting continuous loss amounts into discrete bins with specific boundaries and probability masses, the method changes the mathematical representation from continuous random variables to discrete probability distributions. This parameter transformation enables exact calculation of loss distribution without relying on Monte Carlo sampling, thereby guaranteeing accuracy while simplifying the computational approach.

The patent performs preliminary discretization of the scale distribution into upper and lower bound distributions before calculating the composite loss distribution. By pre-defining discrete bins and their associated probability masses, the method prepares the computational framework in advance, allowing for efficient calculation of the final loss distribution. This preliminary action eliminates the need for iterative Monte Carlo simulations, reducing calculation time while ensuring accuracy through deterministic bound calculations.

The patent calculates both upper and lower bound sub-composite distributions, which is more computation than a single-point estimate would require. However, this excessive action provides guaranteed accuracy bounds and enables the determination of the true loss distribution within a known error margin. The dual-bound approach ensures that the actual loss distribution lies within the calculated bounds, providing rigorous accuracy guarantees that justify the additional computational effort.