PiecewisePareto_ML_Estimator_Alpha | R Documentation |

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

```
PiecewisePareto_ML_Estimator_Alpha(
losses,
t,
truncation = NULL,
truncation_type = "lp",
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 vector. Thresholds of the piecewise Pareto distribution. |

`truncation` |
Numeric. If |

`truncation_type` |
Character. 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 (only used in truncated case). |

`alpha_max` |
Numeric. Upper bound for the estimated alphas (only used in truncated case). |

Maximum likelihood estimator for the parameter `alpha`

of a Pareto distribution with threshold `t`

given the observations `losses`

```
losses <- rPiecewisePareto(10000, t = c(100,200,300), alpha = c(1,2,3))
PiecewisePareto_ML_Estimator_Alpha(losses, c(100,200,300))
losses <- rPiecewisePareto(10000, t = c(100,200,300), alpha = c(1,2,3),
truncation = 500, truncation_type = "wd")
PiecewisePareto_ML_Estimator_Alpha(losses, c(100,200,300))
PiecewisePareto_ML_Estimator_Alpha(losses, c(100,200,300),
truncation = 500, truncation_type = "wd")
reporting_thresholds <- rPareto(10000, 100, 3)
index <- losses > reporting_thresholds
losses <- losses[index]
reporting_thresholds <- reporting_thresholds[index]
PiecewisePareto_ML_Estimator_Alpha(losses, c(100,200,300),
truncation = 500, truncation_type = "wd")
PiecewisePareto_ML_Estimator_Alpha(losses, c(100,200,300),
truncation = 500, truncation_type = "wd",
reporting_thresholds = reporting_thresholds)
losses <- c(140, 240, 490, 200, 110, 710, 120, 190, 210, 310)
w <- rep(1, length(losses))
w[1] <- 2
losses2 <- c(losses, losses[1])
PiecewisePareto_ML_Estimator_Alpha(losses, c(100,200,300), weights = w)
PiecewisePareto_ML_Estimator_Alpha(losses2, c(100,200,300))
```

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