Abstract
The validity of the Poisson and the
P(k) modified Poisson statistical density functions of observing k events in a short time interval 
t=T/n, proposed previously by others, is investigated experimentally in radioactive decay detection for various measuring times, T. The experiments to measure radioactive decay were performed with 89my (T1/2=16.06 s), using a multichannel analyzer operating in the multiscaling mode. According to the results, Poisson statistics adequately describes the counting experiment for short measuring times (up to T<
0.5 T1/2) and its application is recommended. However, analysis of the data demonstrated, with confidence, that for long measurements (T>1 T1/2) Poisson distribution is not valid and the modified Poisson function is preferable.
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