A Statistical Reanalysis of the Classical Rutherford's Experiment

Abstract

Modified chi-squared and some newly developed tests for the Poisson, binomial, and an approximated Feller's distribution 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. Tests used show that the data contradict to both Poisson and binomial distribution and do not contradict to a precise “binomial” approximation of Feller's distribution that takes into account a counter's dead time. This gives a plausible statistically correct confirmation of the well-established exponential law of radioactive decay.

Keywords:

• Binomial distribution
• Cramér–von Mises tests
• Feller's distribution
• Modified chi-squared tests
• Moment type estimators
• Poisson distribution
• Rutherford's experiment

Mathematics Subject Classification:

• 62F03
• 62P35

Acknowledgments

The authors are grateful to N. Balakrishnan, N. Pya, and the referees, for their numerous valuable comments and suggestions that greatly helped to improve this article.