Abstract
This paper introduces a new one-parameter discrete distribution, namely L-geometric-discrete Rayleigh (LGDR) distribution. This distribution mixes geometric and discrete Rayleigh distributions by using Lindley weights. Basic statistical and reliability properties of this model are derived and presented. Maximum likelihood and method of moments estimation procedures for the underlying parameter are calculated and simulated for different values of the parameter and for different sample sizes. The reliability function is also derived using the stress-strength model. The model is fitted to three different datasets, which demonstrates that this new model can provide a better fit than some known distributions. The likelihood ratio test and the Kolmogorov-Smirnov statistic are used to test this fit.