Pareto_Find_Alpha_btw_FQs function

Pareto Alpha Between Two Frequencies

Finds the Pareto alpha between two excess frequencies

Pareto_Find_Alpha_btw_FQs(
  Threshold_1,
  Frequency_1,
  Threshold_2,
  Frequency_2,
  max_alpha = 100,
  tolerance = 1e-10,
  truncation = NULL
)

Arguments

• Threshold_1: Numeric. Threshold 1
• Frequency_1: Numeric. Expected frequency in excess of Threshold_1
• Threshold_2: Numeric. Threshold 2
• Frequency_2: Numeric. Expected frequency in excess of Threshold_2
• max_alpha: Numeric. Upper limit for the alpha that is returned.
• tolerance: Numeric. Accuracy of the result.
• truncation: Numeric. If truncation is not NULL then the Pareto distribution is truncated at truncation.

Returns

The Pareto alpha between the expected number of claims Frequency_1 excess Threshold_1

and the expected number of claims Frequency_2 excess Threshold_2

Examples

Pareto_Find_Alpha_btw_FQs(1000, 1, 2000, 0.5)
Pareto_Find_Alpha_btw_FQs(1000, 1, 2000, 0.5, truncation = 5000)

References

Riegel, U. (2018) Matching tower information with piecewise Pareto. European Actuarial Journal 8(2): 437--460