Two distributions, such as, simple Lagrange-negative binomial (SLNB) distribution and weighted Lagrange-negative binomial (WLNB) distribution are dealt with. It is shown that either one of them can be analyzed it terms of the other and no separate analysis for each is necessary. For this purpose, a series of recurrence relations in moments are obtained connecting both SLNB and WLNB. Next, some other functions of moments including inverse moments are given. Also some relations in ordinates are given. Finally, estimation of the parameters is taken up.