Discrete Generalized Odd Lindley–Weibull Distribution with Applications

In this paper, we introduce a new probability mass function by discretizing the continuous failure model of the generalized odd Lindley–Weibull distribution, which is called the discrete generalized odd Lindley–Weibull (DGOL-W) distribution. This new probability mass function is characterized by a very flexible probability function: reverse J-shape, right-skewed shape, left-skewed shape, and close to symmetric shape. The proposed distribution has five special models, i.e., the discrete generalized odd Lindley-exponential, discrete generalized odd Lindley–Rayleigh, discrete odd Lindley–Weibull, discrete odd Lindley-exponential, and discrete odd Lindley–Rayleigh distributions. Some properties of the proposed distribution are introduced. The maximum likelihood estimation is used to estimate the unknown parameters of the DGOL-W distribution. Applications are illustrated, which show that the model is suited for use in various data sets, i.e., the mean and variance of the count data are equal, over-dispersion count data, and under-dispersion count data. Based on the results, we have shown that the DGOL-W distribution provides a better fit compared to the Poisson, discrete Lindley and four sub-models of DGOL-W distribution for count data.