Summary
It is shown that a certain estimator, applied in the physical sciences to counts of particles, is in general inconsistent: it need not and, normally, does not converge in probability towards the true value of the estimated number; it converges, however, towards a lower bound of it. By splitting the process of counting into suitable sub-counts, it appears possible to overcome this difficulty.
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Kurth, R. Counting as a sequence of bernoulli trials. Metrika 9, 149–152 (1965). https://doi.org/10.1007/BF02614176
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DOI: https://doi.org/10.1007/BF02614176