# Probability of detecting a feature that covers a proportion theta of the survey area.

### Description

The function can calculate the probability of a feature that occupies
a proportion `theta`

of the sampling area and where the sampling point density of the survey is
specified; the sampling point density needed to achieve a specified probability of detection, where
`theta`

is also specified ; or the value of `theta`

that will be detected with specified
probability and sampling density.Unless the feature is made of a large number of random segments
(see below for how to deal with this situation), these methods apply only when the pattern of points
in the sampling deisgn is random.

### Usage

1 | ```
detect.prop(statistic, theta=NA, pdetect=NA, ssize=NA)
``` |

### Arguments

`statistic` |
Describes what aspect of design you want calculated. The choices are |

`theta` |
Feature proportion. Not needed if |

`pdetect` |
Probability detection. Not needed if |

`ssize` |
Sample size. Not needed if |

### Details

The probability of detection is `p = 1 - (1 - theta)^{N}`

. Formulae for `theta`

and
`N`

are readily obtained from this formula. If the spatial pattern of the feature consists of lots of small,
random uniformly distributed fragments, then we can redefine `theta = Na/A`

where `a`

is the
area of the sampling unit and `A`

is the sampling area.In this situation, the probability of patch detection
applies no matter what the spatial pattern of points in the sampling design. Unlike `detect`

, `detect.prop`

works for vectors - so long as the input vectors are of the same length.

### Value

`prob` |
Probability of detection |

`ssize` |
Sample size |

`prop` |
Feature proportion |

### Author(s)

Jon Barry: Jon.Barry@cefas.co.uk

### Examples

1 2 3 | ```
detect.prop(statistic='P', theta=0.02, ssize=80)
detect.prop(statistic='N', theta=0.02, pdetect=0.9)
detect.prop(statistic='F', pdetect=0.9, ssize=80)
``` |