The binomial distribution describes the probability of the number of successes\nfor a fixed number of identical independent experiments, each with binary\nout-put. In real life, practical applications like portfolio credit risk management\ntrials are not identical and have different realization probabilities. In\naddition to the number, the quantitative impacts of the respective outputs are\nalso important. There exist no complete model-side implementations for the\nexpansion of the binomial distribution, especially not in the case of specific\nquantitative parameters up to now. Here, a solution of this issue is described by\nthe extended binomial distribution. The key for solving the problem lies in the\nuse of bijection between the elementary events of the binomial distribution\nand the digit sequences of binary numbers. Based on the extended binomial\ndistribution, an analytical portfolio credit risk model is described. The binomial\ndistribution approach minimizes the approximation error in modeling.\nIn particular, the edges of the loss distribution can be determined in a\nrealistic manner. This analytical portfolio credit risk model is especially predestined\nfor management of risk concentrations and tail risks.
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