Distribution Name: Truncated Power Law
Parameters:
- Alpha (Shape parameter)
- Theta (Location parameter)
- T (Truncated limit)
The truncated power law distribution mirrors the power law distribution, but with an upper limit that is imposed by the user. While the heavy tail of the power law distribution allows us to account for the rare catastrophic event, there may be a theoretical bound to the size of such an event. If this upper limit is not factored into the model, we may produce a misleading and unnecessarily grim forecast.
- When to Use: The power law distribution should be truncated if an upper bound on the severity of an event is known.
- Example: Losses of records may follow a power law but you know you only have a finite number of records to lose.
- Excel Formula: =(alpha*theta^alpha/(x^(alpha+1)))/(1-(theta/T)^alpha)
- Mean: =(alpha*theta/(alpha-1))