# Post-calving method for caribou abundance estimation

### Description

The function `abundance`

applies the methodology found in Rivest et al. (1998) for estimating
caribou abundance using postcalving aggregations detected by radio telemetry.

### Usage

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### Arguments

`mat` |
A matrix containing in the first column the number of radio-collared animals in the detected (photographed) groups and in the second column the corresponding size of the detected groups. |

`n` |
A numeric: the total number of active collars during the census. |

`model` |
A character string indicating the model to determine the probability that a group with
collared animals is detected |

`B` |
A numeric: a bound for the threshold model. |

`maxT.hat` |
A numeric: an upper bound used in the numerical computation of |

`x` |
An object, produced by the |

`...` |
Further arguments to be passed to methods (see |

### Details

DETECTION MODELS

**- homogeneity model** (`model="H"`

):

*pi = r if xi>=1*

**- independence model** (`model="I"`

):

*pi = 1-(r^xi)*

**- threshold model** (`model="T"`

):

*pi = 1 if xi>=B, r if 1<=xi<B*

where *pi* is the probability that a group with collared animals is detected,
*xi* is the number of radio-collared in the detected (photographed) groups and
*r* is a parameter related to the probability of detection.
For the threshold model, `B`

is a bound given as a function's argument.

### Value

`mp ` |
The number of detected groups having radio-collared animals. |

`xt ` |
The total number of radio-collared animals found in the detected groups. |

`gnt ` |
The total number of animals counted in the detected groups. |

`rr ` |
The estimated parameter related to the probability of detection. |

`se_rr ` |
The estimated standard error of |

`mat_pi ` |
A matrix containing a sorted copy of the input matrix |

`T.hat ` |
The estimator for the total number of animals in a herd. |

`se_T.hat ` |
The estimated standard error of |

`loglikelihood ` |
The maximum value of the loglikelihood function for the detected model. |

`randomness_test ` |
A vector with the statistic and the p-value of a score test for the randomness assumption available only for the homogeneity, independence and threshold model with B=2 or 3. |

`call ` |
The function call (object of class "call"). |

### Author(s)

Helene Crepeau Helene.Crepeau@mat.ulaval.ca and

Louis-Paul Rivest Louis-Paul.Rivest@mat.ulaval.ca and

Serge Couturier tuttu@videotron.ca and

Sophie Baillargeon Sophie.Baillargeon@mat.ulaval.ca

### References

Rivest, L.-P., Couturier, S. and Crepeau, H. (1998). Statistical Methods for estimating caribou abundance
using postcalving aggregations detected by radio telemetry. *Biometrics*, **54**(3), 865-876.

### See Also

`petersen`

### Examples

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