New and fast closed-form efficient estimators for the negative multinomial distribution

Jun Zhao, Yun-beom Lee and Hyoung-Moon Kim

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 20, 6684-6699

Abstract: The negative multinomial (NM) distribution is of interest in various application studies. Based on closed-form n-consistent estimators, new and fast closed-form efficient estimators are proposed for the NM distribution. The theorem applied to derive the new estimators guarantees two important properties of the new closed-form efficient estimators: asymptotic efficiency and normality. The new closed-form efficient estimators are denoted as MLE-CEs, because the asymptotic distribution is the same as that of the maximum likelihood estimators (MLEs). Simulation studies suggest that the MLE-CE performs similarly to its MLE. The estimated accuracies of the MLE and MLE-CE are generally better than the method of moments estimator (MME) for relatively large 𝒑 values. The MLE-CE is 10–30 times faster than the MLE, especially for large sample sizes, which is good for the big data era. Considering the estimated accuracy and computing time, the MLE-CE is recommended for large 𝒑 values, whereas the MME is recommended for other conditions.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2025.2461610 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:54:y:2025:i:20:p:6684-6699

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2025.2461610

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().