  A discrete-time stochastic process derived from a model of basketball is used
to generalize any discrete distribution. The generalized distributions can have
one or two more parameters than the parent distribution. Those derived from
binomial, Poisson and negative binomial distributions can be underdispersed or
overdispersed. The mean can be simply expressed in terms of model parameters,
thus making inference for the mean straightforward. Probabilities can be
quickly computed, enabling likelihood-based inference. Random number generation
is also straightforward. The properties of some of the new distributions are
described and their use is illustrated with examples.
