A Discrete Gumbel Distribution

Abstract: 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.