  In this paper, we obtain Stein operator for sum of $n$ independent random
variables (rvs) which is shown as perturbation of negative binomial (NB)
operator. Comparing the operator with NB operator, we derive the error bounds
for total variation distance by matching parameters. Also, three parameters
approximation for such a sum is considered and is shown to improve the existing
bounds in the literature. Finally, an application of our results to a function
of waiting time for $(k_1,k_2)$-events is given.
