# 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) |