GenPareto_ML_Estimator_Alpha | R Documentation |

Calculates the maximum likelihood estimators of the parameters alpha_ini and alpha_tail of a generalized Pareto distribution with known threshold and (if applicable) known truncation

```
GenPareto_ML_Estimator_Alpha(
losses,
t,
truncation = NULL,
reporting_thresholds = NULL,
is.censored = NULL,
weights = NULL,
alpha_min = 0.001,
alpha_max = 10
)
```

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

`t` |
Numeric or numeric vector. Threshold of the generalized Pareto distribution. Alternatively, |

`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 the estimated alphas. |

`alpha_max` |
Numeric. Upper bound for the estimated alphas. |

Maximum likelihood estimator for the parameters `alpha_ini`

and `alpha_tail`

of a generalized Pareto distribution with threshold `t`

given the observations `losses`

```
losses <- rGenPareto(1000, 1000, 2,3)
GenPareto_ML_Estimator_Alpha(losses, 1000)
losses <- rGenPareto(1000, 1000, 2, 1, truncation = 10000)
GenPareto_ML_Estimator_Alpha(losses, 1000)
GenPareto_ML_Estimator_Alpha(losses, 1000, truncation = 10000)
t <- 1000
alpha_ini <- 1
alpha_tail <- 3
losses <- rGenPareto(5000, t, alpha_ini, alpha_tail)
reporting_thresholds <- rPareto(5000, 1000, 3)
reported <- losses > reporting_thresholds
losses <- losses[reported]
reporting_thresholds <- reporting_thresholds[reported]
GenPareto_ML_Estimator_Alpha(losses, t)
GenPareto_ML_Estimator_Alpha(losses, t, reporting_thresholds = reporting_thresholds)
limit <- 3000
censored <- losses > limit
losses[censored] <- limit
reported <- losses > reporting_thresholds
losses <- losses[reported]
censored <- censored[reported]
reporting_thresholds <- reporting_thresholds[reported]
GenPareto_ML_Estimator_Alpha(losses, t, reporting_thresholds = reporting_thresholds)
GenPareto_ML_Estimator_Alpha(losses, t, reporting_thresholds = reporting_thresholds,
is.censored = censored)
losses <- c(190, 600, 120, 270, 180, 120)
w <- rep(1, length(losses))
w[1] <- 3
losses2 <- c(losses, losses[1], losses[1])
GenPareto_ML_Estimator_Alpha(losses, 100, weights = w)
GenPareto_ML_Estimator_Alpha(losses2, 100)
```

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