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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to extreme value theory

A GEV distribution has μ = 50, σ = 10 and ξ = -0.5. What is the upper endpoint of its support?

For a negative shape parameter the GEV has a finite upper endpoint at μ - σ/ξ. With μ = 50, σ = 10 and ξ = -0.5 this is 50 + 20 = 70. A finite endpoint exists because ξ is negative, the Weibull-type case.

  1. A70Correct
  2. B60
  3. C50
  4. D90
  5. There is no finite endpoint

Explanation

For ξ < 0, the support is bounded above by μ - σ/ξ. Here 50 - 10/(-0.5) = 50 + 20 = 70. Option D uses 50 + 4σ, which is not the formula. Option E would apply only for ξ ≥ 0.

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