Description Usage Arguments Value Examples

Calculates the maximum likelihood estimator for the parameter alpha of a Pareto distribution with a known threshold and (if applicable) a known truncation

1 2 3 4 5 6 7 8 9 10 |

`losses` |
Numeric vector. Losses that are used for the ML estimation. |

`t` |
Numeric. Threshold of the Pareto distribution. |

`truncation` |
Numeric. If |

`reporting_thresholds` |
Numeric vector. Allows to enter loss specific reporting thresholds. If |

`is.censored` |
Logical vector. |

`weights` |
Numeric vector. Weights for the losses. For instance |

`alpha_min` |
Numeric. Lower bound for alpha (only used in truncated case). |

`alpha_max` |
Numeric. Upper bound for alpha (only used in truncated case). |

Maximum likelihood estimator for the parameter `alpha`

of a Pareto distribution with threshold `t`

given the observations `losses`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
losses <- rPareto(100, 1000, 2)
Pareto_ML_Estimator_Alpha(losses, 1000)
losses <- rPareto(100, 1000, 2, truncation = 2000)
Pareto_ML_Estimator_Alpha(losses, 1000)
Pareto_ML_Estimator_Alpha(losses, 1000, truncation = 2000)
t <- 100
alpha <- 2
losses <- rPareto(10000, t, alpha)
reporting_thresholds <- rPareto(10000, t, 5)
index <- losses > reporting_thresholds
losses <- losses[index]
reporting_thresholds <- reporting_thresholds[index]
Pareto_ML_Estimator_Alpha(losses, t)
Pareto_ML_Estimator_Alpha(losses, t, reporting_thresholds = reporting_thresholds)
losses <- rPareto(10, 1000, 2)
w <- rep(1, 10)
w[1] <- 3
losses2 <- c(losses, losses[1], losses[1])
Pareto_ML_Estimator_Alpha(losses, 1000, weights = w)
Pareto_ML_Estimator_Alpha(losses2, 1000)
``` |

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