Remarks on and Characterizations of 2S-Lindley and 2D-Lindley Distributions Introduced by Chesneau et al.(2020)

Chesneau et al.(2020) considered the distributions of sum and differences of two independent and identically distributed random variables with the common Lindley distribution. They derived, very nicely, the above mentioned distributions and provided certain important mathematical and statistical properties as well as simulations and applications of the new distributions. In this short note, we like to show that the assumption of "independence" can be replaced with a much weaker assumption of "sub-independence". Then we present certain characterizations of the proposed distributions to complete, in someway, their work.