Modified Skellam, Poisson and Gaussian distributions in semi-open systems at charge-like conservation law

Abstract: A modification of the Skellam and Poisson distributions is proposed for subsystems when the constraints imposed by the charge conservation law in the complete system are taken into account. Such distributions can be applied, for example, for an analysis of the fluctuations of baryon and net baryon numbers in certain pseudo-rapidity interval in $A+A$ and $p+p$ collisions with high multiplicities. The presented modified Skellam, Poisson and Gaussian distributions can be utilized also in various branches of science, when one studies the fluctuations of the two variables related to a subsystem, as well as the distribution of the difference of these variables, while the mentioned difference in the total system is fixed.