### Abstract

The binomial, Poisson and modified Poisson models which are used for describing the statistical nature of the distribution of counts are compared theoretically, and conclusions for application are considered. The validity of the Poisson and the modified Poisson statistical distribution for observing k events in a short time interval is investigated experimentally for various measuring times. The experiments to measure the influence of the significant radioactive decay were performed with ^{189}Y^{m89}Y^{m}(T_{ 1 2} = 16.06 s), using a multichannel analyser (4096 channels) in the multiscaling mode. According to the results, Poisson statistics describe the counting experiment for short measuring times (up to T = 0.5T_{ 1 2}) and its application is recommended. However, analysis of the data demonstrated, with confidence, that for long measurements (T ≥ T_{ 1 2}) Poisson distribution is not valid and the modified Poisson function is preferable. The practical implications in calculating uncertainties and in optimizing the measuring time are discussed. Differences between the standard deviations evaluated on the basis of the Poisson and binomial models are especially significant for experiments with long measuring time (T/T_{ 1 2} ≥ 2) and/or large detection efficiency (ε > 0.30). Optimization of the measuring time for paired observations yields the same solution for either the binomial or the Poisson distribution.

Original language | English |
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Pages (from-to) | 591-597 |

Number of pages | 7 |

Journal | Nuclear Inst. and Methods in Physics Research, A |

Volume | 312 |

Issue number | 3 |

DOIs | |

Publication status | Published - Feb 15 1992 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Instrumentation

### Cite this

*Nuclear Inst. and Methods in Physics Research, A*,

*312*(3), 591-597. https://doi.org/10.1016/0168-9002(92)90209-M