This article is concerned with proposing a discrete version of a competing risks model, namely, the Pham–Burr XII distribution, via the general approach of discretization. The proposed model’s probability mass function displays decreasing, unimodal and decreasing–unimodal patterns, while its hazard rate and alternative hazard rate functions exhibit different and important shapes, which are decreasing, bathtub (Vtub), modified bathtub and unimodal shapes. Through these shapes, the flexibility and diversity in shapes of the characteristic functions of the discrete Pham–Burr XII distribution can be demonstrated. Therefore, the discrete Pham–Burr XII distribution can provide a better fit for several types of discrete data and count data. The main characteristic functions of the discrete Pham–Burr XII distribution are derived, and its properties are studied. Moreover, the parameters and the main characteristic functions of the discrete Pham–Burr XII distribution are estimated via the maximum likelihood method. Also, the asymptotic confidence intervals and percentile bootstrap confidence intervals are considered. Moreover, point and interval estimation of some entropy measures is discussed. Furthermore, a simulation study is achieved to assess the performance of the delivered maximum likelihood estimates. Finally, the applicability of the discrete Pham–Burr XII distribution is examined though different applications.
Salem et al. (Mon,) studied this question.