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