the exponentiated discrete inverse rayleigh distribution

In this paper, a new distribution called the exponentiated discrete inverse rayleigh distribution is introduced, which isan extension of the discrete inverse rayleigh distribution. this new discrete distribution is a discrete analogue of the continuous exponentiated inverse rayleigh distribution. in this paper, we discuss the shapes of probability mass and hazard rate functions, the moments of the new distribution and data generation. the maximum likelihood estimation of the parameters is also studied. finally, an example is given to demonstrate an application of the new distribution.