The method of eliminating the interfering parameter in the statistics of the Poisson flow of points

Comparison of the total number of registered tracks with the estimates of the number of tigers available in the literature showed the presence of significant differences in the territory of Primorsky Krai. To eliminate possible errors, the source data is represented by an inhomogeneous point Poisson flow. The problem of processing data on the calculation of the population density of the Amur tiger in the regions of Primorsky Krai is considered. The primary basis for this calculation was the author's sample of information on the registration of predator tracks in winter. The working method of trace accounting is modeled by the procedure of coloring flow points depending on the probability of trace detection. This probability becomes an interfering parameter, which is eliminated by replacing the number of traces with the proportion of traces in different areas. The theorem on the convergence of the fraction of traces to the limiting value is proved when the parameter of the Poisson distribution characterizing the total number of traces tends to infinity. The results obtained are illustrated by a map characterizing the estimated proportions of Amur tiger tracks in the Primorsky Territory for the accounting period of 2005. Contribution of the authors: the authors contributed equally to this article. Tsitsiashvili G.Sh. developed the mathematical part of the article. Bocharnikov V.N. formulated a meaningful statement of the problem and providedfactual material. Krasnopeev S.M. presented the results of calculations in the form of a map. The authors declare no conflicts of interests.

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