## Eberhardt’s Statistic :

Eberhardt’s statistic is a measure of the effectiveness of a classification model, specifically a binary classification model (a model that assigns data points to one of two classes). The statistic is calculated by dividing the difference between the true positive rate (TPR) and the false positive rate (FPR) by the true positive rate.

For example, suppose we have a binary classification model that is designed to identify individuals who have a certain disease. The model looks at various factors, such as age, gender, and medical history, and uses this information to predict whether an individual has the disease or not.

The true positive rate (TPR) is the proportion of individuals with the disease who are correctly identified by the model as having the disease. For example, if the model correctly identifies 80 out of 100 individuals with the disease, then the TPR would be 80%.

The false positive rate (FPR) is the proportion of individuals without the disease who are incorrectly identified by the model as having the disease. For example, if the model incorrectly identifies 20 out of 100 individuals without the disease as having the disease, then the FPR would be 20%.

To calculate Eberhardt’s statistic, we simply divide the difference between the TPR and FPR by the TPR. In our example, this would be (80% – 20%) / 80% = 75%.

This means that the model is 75% effective at correctly identifying individuals with the disease, while also minimizing the number of false positives (individuals without the disease who are incorrectly identified as having the disease).

Another example of Eberhardt’s statistic would be a model designed to identify fraudulent credit card transactions. In this case, the TPR would be the proportion of fraudulent transactions that are correctly identified by the model, and the FPR would be the proportion of legitimate transactions that are incorrectly identified as fraudulent. By dividing the difference between these rates by the TPR, we can determine the effectiveness of the model in identifying fraudulent transactions while minimizing the number of false positives.

Eberhardt’s statistic is a useful measure of the effectiveness of binary classification models because it takes into account both the true positive rate and the false positive rate, providing a more complete picture of the model’s performance. It is especially useful in applications where it is important to minimize the number of false positives, such as medical diagnosis or fraud detection.