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Generalized Pareto Distribution
3.23. Generalized Pareto Distribution
Does @RISK handle a generalized Pareto distribution?
Yes, with the restriction that the shape parameter must be positive.
The generalized Pareto distribution takes three parameters: location μ (mu), scale σ (sigma), and shape k. The RiskPareto2 distribution takes three parameters: scale b, shape q, and optionally a location shift in the RiskShift( ) property function.
Conversion between the parameters:
- scale: b = σ/k or σ = b/q
- shape: q = 1/k or k = 1/q
- location: μ = RiskShift value
Conversion between the functions:
- GPD(μ, σ, k) is equivalent to RiskPareto2(σ/k, 1/k, RiskShift(μ))
- RiskPareto(b, q, RiskShift(μ)) is equivalent to GPD(b/q, 1/q, RiskShift(μ))
last edited: 2012-06-15