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This article gives a probabilistic overview of the widely used method ofdefault probability estimation proposed by K. Pluto and D. Tasche. There arelisted detailed assumptions and derivation of the inequality where theprobability of default is involved under the influence of systematic factor.The author anticipates adding more clarity, especially for early careeranalysts or scholars, regarding the assumption of borrowers' independence,conditional independence and interaction between the probability distributionssuch as binomial, beta, normal and others. There is also shown the relationbetween the probability of default and the joint distribution of$\sqrt{\varrho}X-\sqrt{1-\varrho}Y$, where $X$, including but not limiting, isthe standard normal, $Y$ admits, including but not limiting, the beta-normaldistribution and $X,\,Y$ are independent.

Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche