The Discrete Half-Normal Distribution

Abstract

The discrete half-normal distribution is derived as the maximum entropy distribu- tion on 0,1, . . . with specified mean and variance. It is a limiting q-hyper-Poisson-I distribution that arises from the Morse M/M/1 queue with service-dependent balk- ing. Success runs models are reviewed. A new derivation as a mixture of Heine distributions is given. Finally the moment and other properties are examined.