Discrete generalized rayleigh distribution

In this paper,a new two-parameter discrete distribution is introduced which is in fact an analogue of the continuous generalized rayleigh distribution,called discrete generalized rayleigh distribution. the one parameter discrete rayleigh distribution is obtained as a particular case. several important distributional and reliability properties such as survival and hazard rate functions,moments,order statistics,unimodality and infinite divisibility of the proposed distribution are examined. a related characterization of the distribution is also provided. parameter estimation,using different methods,namely methods of moments,maximum likelihood and proportion,is discussed. performance of the different estimation methods are compared by means of a monte carlo simulation. finally,two real data sets are analyzed to investigate the suitability of the proposed distribution in modeling count data. © 2016 pakistan journal of statistics.