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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 conditions. Detection probability appearing to increase or remain constant with distance from the transect line may indicate problems with data collection or survey design.<ref name=buckland2001/>
===Covariates===
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===Series expansions===
A frequently used method to improve the fit of the detection function to the data is the use of series expansions. Here, the function is split into a "key" part (of the type covered above) and a "series" part; i.e., g(''y'') = key(''y'')[1 + series(''y'')]. The series generally takes the form of a [[polynomial]] (e.g. a [[Hermite polynomials|Hermite polynomial]]) and is intended to add flexibility to the form of the key function, allowing it to fit more closely to the data PDF. While this can improve the precision of density/abundance estimates, its use is only defensible if the data set is of sufficient size and quality to represent a reliable estimate of detection distance distribution. Otherwise there is a risk of [[overfitting]] the data and allowing non-representative characteristics of the data set to bias the fitting process.<ref name=buckland2001/><ref name=buckland2004>{{cite book|last=Buckland|first=S. T.|year=2004|title=Advanced distance sampling|publisher=Oxford University Press}}</ref>
==Assumptions and sources of bias==
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==Software implementations==
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== References ==
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