Sequential negative binomial problems and statistical ecology: A selected review with new directions

We begin by selectively reviewing a majority of influential research methods for a number of formulations and their executions in the context of fixed-sample-size inferential procedures (Section  2). Subsequently, we elaborate on purely sequential and two-stage sampling methodologies for data collection (Sections  3 and 4). In Section  5, we summarize some major results with their interpretations including large-sample first- and second-order properties as appropriate. The illustrations of all the sequential inferential procedures on the real dataset gives interesting insights (Section  6). We also propose a number of selected directions for future research of substantial nature (Section  7). Finally, our own R codes are provided in the Appendix.