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I was reading the paper: "Estimating Probabilities of Default for Low Default Portfolios" by Katja Pluto and Dirk Tasche and they mention the following:

The tail distribution of a binomial distribution can be expressed in terms of an appropriate beta distribution function.

I have not so much knowledge of statistics, is it possible someone could explain to me why is this the case? Thank you very much!

Laura González Gaitán
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  • Basically, the shape of the binomial distribution can be well approximated by a scaled beta distribution with the right parameters. This is especially useful for low or high probabilities of response where the shape of the binomial distribution is far from normal. – AdamO Mar 30 '21 at 17:33
  • @AdamO This is not an approximation: it refers to the exact relation between the two distributions. – whuber Mar 30 '21 at 17:47

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