Table 8 Probabilities of solvency in the case the risk capital is calculated without taking parameter uncertainty into account for \(n=20\) and different confidence levels, continuous distributions and methods of estimation, determined using a Monte-Carlo simulation with 10,000,000 simulations

From: Practical aspects of modelling parameter uncertainty for risk capital calculation

n Distribution Estimation \(95\%\) \(99\%\) \(99.5\%\)
method
True parameter
20 Gamma ML 93.16% 97.86% 98.63%
\(k=0.5\), \(\beta=1\)
ML 93.27% 98.00% 98.76%
\(k=2\), \(\beta=1\)
MM 92.60% 97.41% 98.26%
\(k=0.5\), \(\beta=1\)
MM 93.26% 97.96% 98.72%
\(k=2\), \(\beta=1\)
Normal/ ML* 93.29% 98.03% 98.79%
Lognormal
(two parameter)
  MM 93.26% 98.02% 98.78%
  \(\mu=0.1\), \(\sigma=0.1\)
Normal/ MM 93.26% 98.02% 98.78%
Lognormal \(\mu=1\), \(\sigma=0.1\)
  MM 91.81% 97.00% 97.98%
  \(\mu=1\), \(\sigma=1\)
Exponential ML* 93.91% 98.42% 99.10%
(one parameter)
Pareto ML* 93.29% 98.14% 98.90%
  (two parameter)