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Abstract:
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Modified chi-squared tests for Poisson, binomial, and approximated Feller's distributions are discussed. A reanalysis of the classical Rutherford's experimental data on alpha decay is done. Previous analyses of the data were not correct from the point of view of the theory of statistical testing. Suggested tests show that the data contradict to both Poisson and binomial distribution and do not contradict to a precise "binomial" approximation of Feller's distribution, which accurately takes into account a counter's dead time. This gives a plausible statistically correct confirmation of the well-established exponential law of radioactive decay. An application of the suggested tests for the analysis of the number of US Supreme Court justices' appointments from 1789 up to date shows that the binomial process has the same right to exist as the Poisson one under use.
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