*Article* **Discrete Pseudo Lindley Distribution: Properties, Estimation and Application on INAR(1) Process**

**Muhammed Rasheed Irshad 1, Christophe Chesneau 2,\*, Veena D'cruz <sup>1</sup> and Radhakumari Maya <sup>3</sup>**


**Abstract:** In this paper, we introduce a discrete version of the Pseudo Lindley (PsL) distribution, namely, the discrete Pseudo Lindley (DPsL) distribution, and systematically study its mathematical properties. Explicit forms gathered for the properties such as the probability generating function, moments, skewness, kurtosis and stress–strength reliability made the distribution favourable. Two different methods are considered for the estimation of unknown parameters and, hence, compared with a broad simulation study. The practicality of the proposed distribution is illustrated in the first-order integer-valued autoregressive process. Its empirical importance is proved through three real datasets.

**Keywords:** Pseudo Lindley distribution; survival discretization method; over dispersion; moments; simulation; maximum likelihood estimation

**MSC:** 62E15; 62E20; 62E17
