Answer: Negative Binomial distribution for frequency, and Pareto distribution for severity.

## Explanation In operational risk modeling using Monte Carlo simulation for aggregate loss distributions: - **Loss Frequency Distribution**: The **Negative Binomial distribution** is commonly used because it allows for overdispersion (variance greater than mean), which better captures the reality that operational loss events may not be independent and can occur in clusters. - **Loss Severity Distribution**: The **Pareto distribution** is widely used for modeling operational loss severity because it has a heavy tail, which is appropriate for capturing extreme loss events that are characteristic of operational risk. **Why other options are incorrect:** - **Option A**: Binomial distribution assumes fixed number of trials and constant probability, which is too restrictive for operational loss frequency. Poisson distribution for severity is inappropriate as it's typically used for frequency modeling. - **Option B**: Lognormal distribution is more appropriate for severity modeling, not frequency. Weibull distribution can be used for severity but is less common than Pareto for operational risk. - **Option D**: Transformed Beta distribution is not standard for frequency modeling. Normal distribution is inappropriate for severity as operational losses are typically right-skewed and cannot be negative. The combination of Negative Binomial for frequency and Pareto for severity represents the standard industry practice in operational risk modeling using the Loss Distribution Approach (LDA).

Author: LeetQuiz .