CONTINUOUS COUNTERPARTS OF POISSON AND BINOMIAL DISTRIBUTIONS AND THEIR PROPERTIES

On the basis of integral representations of Poisson and bi- nomial distribution functions via complete and incomplete Euler - and B-functions, we introduce and discuss continuous counterparts of the Pois- son and binomial distributions. The former turns out to be closely related to classical Volterra functions as well. Under usual condition Np ! , we also prove that the sequence of continuous binomial distributions converges weakly to the continuous Poisson one. At the end, we discuss a relationship between the continuous Poisson distribution and the -process.