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An Implementation of the Burnham-Anderson Distribution-Free Method of Estimating Wildlife Densities from Line Transect Data
C. E. Gates and P. W. Smith
Vol. 36, No. 1 (Mar., 1980), pp. 155-160
Published by: International Biometric Society
Stable URL: http://www.jstor.org/stable/2530506
Page Count: 6
You can always find the topics here!Topics: Density estimation, Estimators, Polynomials, Population estimates, Estimation methods, Biometrics, Statistical estimation, Degrees of polynomials, Histograms, Estimation bias
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Burnham and Anderson (1976, Biometrics 32, 325-336) developed the basis for a distribution-free estimator of population density from line transect data. Without committing themselves to a specific algorithm, they recommended fitting a smooth curve h(·) to the midpoints of a frequency distribution of right-angle sighting distances, then using h(0) to estimate density. In this communication we propose a specific algorithm for fitting a polynomial of degree m to the midpoints of a frequency histogram by minimizing the sum of squared differences between the observed areas of each bar in a histogram and the corresponding integrated area under the curve. It is demonstrated by means of computer simulation that such a procedure can lead to small biases if the degree of the polynomial is not sufficient to estimate the true underlying distribution when it is Negative Exponential, Half-Normal or Triangular. Furthermore, the simulated standard error of the estimate is nearly proportional to the degree of the fitted polynomial. The authors recommend the compromise of a fourth-degree polynomial for which the bias is acceptably small and the coefficient of variation is approximately one percent in samples of right-angle sightings.
Biometrics © 1980 International Biometric Society