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Petersen Estimator (petersen + estimator)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Who captures the marks for the Petersen estimator?

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 3 2007
I. B. J. Goudie
Summary., We examine the claim that the well-known Petersen estimator which is used in population size estimation was not in fact used by the scientist after whom it is named. We show how, in the early years of the last century, the modern use of the Petersen estimator grew from that of the fishing coefficient. Contending with the somewhat conflicting claims that were made at the time, and what by modern standards is poor referencing of sources, we investigate where the credit lies for these concepts, and the principles and protocols which support them. We assess also how far attributions of credit were affected by practical considerations, and the history of the estimator by the nature of the problems being pursued. We identify scientists whose early work on marking and estimating fish populations deserves more credit than it has received. [source]

Double-Observer Line Transect Methods: Levels of Independence

BIOMETRICS, Issue 1 2010
Stephen T. Buckland
Summary Double-observer line transect methods are becoming increasingly widespread, especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain. The resulting data supplement conventional distance sampling data with two-sample mark,recapture data. Like conventional mark,recapture data, these have inherent problems for estimating abundance in the presence of heterogeneity. Unlike conventional mark,recapture methods, line transect methods use knowledge of the distribution of a covariate, which affects detection probability (namely, distance from the transect line) in inference. This knowledge can be used to diagnose unmodeled heterogeneity in the mark,recapture component of the data. By modeling the covariance in detection probabilities with distance, we show how the estimation problem can be formulated in terms of different levels of independence. At one extreme, full independence is assumed, as in the Petersen estimator (which does not use distance data); at the other extreme, independence only occurs in the limit as detection probability tends to one. Between the two extremes, there is a range of models, including those currently in common use, which have intermediate levels of independence. We show how this framework can be used to provide more reliable analysis of double-observer line transect data. We test the methods by simulation, and by analysis of a dataset for which true abundance is known. We illustrate the approach through analysis of minke whale sightings data from the North Sea and adjacent waters. [source]