  A discrete version of the Gumbel (Type I) extreme value distribution has been
derived by using the general approach of discretization of a continuous
distribution. Important distributional and reliability properties have been
explored. It has been shown that depending on the choice of parameters the
proposed distribution can be positively or negatively skewed; possess long
tail(s), and exhibits equal, over or under dispersion. Log concavity of the
distribution and consequential results has been established. Estimation of
parameters by method of maximum likelihood, method of moments, and method of
proportions has been presented. A method of checking model adequacy and
regression type estimation based on empirical survival function has also been
examined. Simulation study has been carried out to check the efficacy of the
maximum likelihood estimators. Finally, the proposed distribution has been
applied to model three real life count data regarding maximum flood discharges
and annual maximum wind speeds from literature.
