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Common methods to calculate confidence band for binomial distribution

The textbook confidence interval for binomial trial is given by

\(CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{\tilde{n}}}\)

It is widely recognizedthat the actual coverage probability of the standard interval is poor for p near 0 or 1.Below are some alternatives that give a much better confidence bands

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Test the performance of a PD model: CAP curve and Accuracy Ratio

In credit risk modeling, the cumulative accuracy profile (CAP) is a way to visualize the discriminative power of a PD model.

The following steps to get a CAP curve

The plot below illustrate a CAP curve. For example, 80% of default occurred amount the population with top 20% of PD,

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What is cross validation?

Cross validation (CV) is a technique to test the effectiveness of a statistical model. To perform CV we need to keep aside a sample/portion of the data on which is do not use to train the model, later us this sample for testing/validating. Below are the few common techniques used for CV.

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Deep copy vs shallow copy in Python

In Python, when you use = to assign an object to a variable, it will simply point the new variable towards the existing object.

The difference between shallow and deep copying is only relevant for compound objects (objects that contain other objects, like lists or class instances):

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