Estimation variances for parameterized marked Poisson processes and for parameterized Poisson segment processes
Tomáš Mrkvička (2004)
Commentationes Mathematicae Universitatis Carolinae
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A complete and sufficient statistic is found for stationary marked Poisson processes with a parametric distribution of marks. Then this statistic is used to derive the uniformly best unbiased estimator for the length density of a Poisson or Cox segment process with a parametric primary grain distribution. It is the number of segments with reference point within the sampling window divided by the window volume and multiplied by the uniformly best unbiased estimator of the mean segment...