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A Gamma-Poisson Distribution of Point to k Nearest Event Distance

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Distance sampling of events in natural or seminatural populations often indicates a larger variance in the distance to the kth nearest event than expected for events distributed completely at random. Overdispersion contributes to the well-known bias problem of distance sampling density estimators. Distance distribution models that accommodate overdispersion in the data should lead to more robust estimators of density. To this end we propose a gamma-Poisson distribution model for distances from a point to k nearest events. The model assumes a gamma distribution of local densities of randomly distributed events. Properties of the distribution and estimation of the parameters and event density are detailed for both constrained and unconstrained sampling. Four examples, one with simulated data from a known negative binomial distribution and three with simulated distance sampling in natural and seminatural stem-mapped tree stands, illustrate the promising performance of this new distribution, both as a model for distances and for density estimation. The modeling approach extends to other mixing distributions.

Keywords: constrained sampling; density estimation; distance sampling; gamma distribution; negative binomial; spatial pattern

Document Type: Research Article

Publication date: 2008-08-01

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
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    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
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