Let $f(t)$ be a characteristic function. The question on infinite divisibility of $g_{2k}(t)=f^{(2k)}(t)/f^{(2k)}(0)$ is considered. There are given the condition for that function not to be infinite divisible. Some examples of infinite divisibility of $g_{2k}(t)$ are given.

Different variants of thinning for discrete random variables are studied. The thinning procedure allows to introduce an analog of scale parameter for positive integer-valued random variables. Sufficient and necessary conditions for the existence of such a scale are given.

This article is devoted to discussing the famous Impact factor citation suited to indicate the published scientific result's significance. Considering this problem based on the available statistical data, we demonstrate that: Impact factor follows a distribution having a heavy power tail that may lead to inconsistency in scientifically comparable journals' evaluation. Further, we remark that many papers recognized as sleeping and seemingly sleeping beauties are not considered when calculating. This makes the impact factor unsuitable in evaluating the original, groundbreaking discoveries and their consequences. Due to permanent changes in the composition of the underlying datasets, the impact factor can not be considered as a reliable indicator and to be used as a consistent evaluation metric. Overall, discussing all represented impact factor obstacles and other appropriate considerations, we conclude that the considered index can hardly be used as a reliable estimator of the publication's significance.

A toy model for the distribution of the impact factor (IF) of a journal is proposed. The model demonstrates the presence of a heavy tail for the IF distribution, which occurs due to some random non-scientific circumstances. Therefore, the use of IF as an indicator of the quality of scientific papers seems to be inadequate.