A multivariate geometric distribution

R. N. Rattihalli

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 24, 8014-8041

Abstract: Based on a multinomial model and times to first occupancies of cells, we define a multivariate geometric distribution. Some examples are given to illustrate the potential application of the distribution. We prove some general results and use them to establish certain properties of the distribution. The joint distribution of minimums over two arbitrary sets of variables is obtained, and as it is a mixture of distributions, we called it a mixed bivariate geometric distribution. By equating the k parameters of the distribution, we define a single-parameter multivariate geometric distribution. Some properties of the minimum and maximum of the components of the defined k-dimensional geometric vector have been investigated. We obtain naive, moment estimators and the maximum likelihood estimator based on the actual observations (not as being done under right censoring in the bivariate case). The maximum likelihood estimator performs better. A test for the distribution to be of a single parameter has been developed. The Fisher information is shown to be more as compared to the one obtained in the bivariate censored case. The proposed model is implemented for the analysis of two bivariate data sets. The model gives a good fit and the hypothesis of equality of parameters is also accepted for both data sets.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2025.2486544 (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:24:p:8014-8041

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

DOI: 10.1080/03610926.2025.2486544

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 ().