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== Detection function ==
[[File:Distance sampling method function fitting basic.png|thumb|right|Half-normal detection function (red line) fitted to PDF of detection data. Data have been collated into distance bands (either collected as such, or combined after collection to improve model fitting). Detection probability decreases with distance from center line (''y'' = 0).]]
The drop-off of detectability with increasing distance from the transect line is modeled using a <b>detection function</b> g(''y'') (here ''y'' is distance from the line). This function is fitted to the distribution of detection ranges represented as a [[probability density function]] (PDF). The PDF is a [[histogram]] of collected distances and describes the probability that an object at distance ''y'' will be detected by an observer on the center line, with detections on the line itself (''y'' = 0) assumed to be certain (''P'' = 1).
By preference, g(''y'') is a [[robust statistics|robust]] function that can represent data with unclear or weakly defined distribution characteristics, as is frequently the case in field data. Several types of functions are commonly used, depending on the general shape of the detection data's PDF:
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Here ''w'' is the overall detection truncation distance and ''a'', ''b'' and ''σ'' are function-specific parameters. The half-normal and hazard-rate functions are generally considered to be most likely to represent field data that was collected under well-controlled condition. In contrast, both the uniform and negative exponential functions assume that detection probability does not drop off from the center line but remains at the same level (uniform) or increases (negative exponential); these circumstances may be indicative of problems with data collection or survey design.<ref name=buckland2001/>
== References ==
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