The pseudo-Lindley distribution was introduced as a useful generalization of the Lindley distribution in Zeghdoudi and Nedjar (2016) who showed interesting properties of their new laws and efficiencies in modeling data in Reliability and Survival Analysis. In this paper we study the estimators of the pair of parameters and determine their asymptotic law from which a chi-square law is derived. From both asymptotic laws, statistical tests are built. Simulation studies on the tests conclude to their efficiency for data sizes generally used in Reliability. R codes related to statistical analysis on that law are given in an appropriate archive repository code paper in Arxiv.