A two-parameter Rayleigh-geometric distribution with increasing-decreasing-increasing and strictly increasing hazard rate characteristics is reviewed. Various properties are discussed and expressed analytically. The estimation of the distribution parameters is studied by the method of maximum likelihood and validated by a simulation study. Numerical examples based on two real data-sets on the waiting time in queue and CO2 emissions are given. The Rayleigh-geometric distribution in this paper has a simpler analytical expression compared to the pre-existing distributions with different parameterizations.
