Certain characterizations of the discrete Lindley and Poisson-Lindley distributions, originally introduced by Bakouch, Jazi Nadarjah (2014) Sankaran (1970), respectively, are presented. Al-Babtain, Gemeay Afify (2020) revisited these distributions provided estimation methods actuarial measures as well their applications in medicine. This short note is intended to complete, some way, (2020)&...