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Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling

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Abstract

Many of the most popular sampling schemes used in forestry are probability proportional to size methods. These methods are also referred to as size-biased because sampling is actually from a weighted form of the underlying population distribution. Length- and area-biased sampling are special cases of size-biased sampling where the probability weighting comes from a lineal or areal function of the random variable of interest, respectively. Often, interest is in estimating a parametric probability density of the data. In forestry, the Weibull function has been used extensively for such purposes. Estimating equations for method of moments and maximum likelihood for two- and three-parameter Weibull distributions are presented. Fitting is illustrated with an example from an area-biased angle-gauge sample of standing trees in a woodlot. Finally, some specific points concerning the form of the size-biased densities are reported.

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Authors and Affiliations

  1. USDA Forest Service, Northeastern Research Station, P.O. Box 640, 271 Mast Road, Durham, NH, 03824

    Jeffrey H. Gove

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  1. Jeffrey H. Gove
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Gove, J.H. Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling. Environmental and Ecological Statistics 10, 455–467 (2003). https://doi.org/10.1023/A:1026000505636

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  • DOI: https://doi.org/10.1023/A:1026000505636

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