Journal of Statistical Theory and Applications

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Volume 17, Issue 4, December 2018, Pages 636 - 646

Efficient Estimator of Parameters of a Multivariate Geometric Distribution

Authors
U. J. Dixit1, *, S. Annapurna2
1Department of Statistics, University of Mumbai, Mumbai, India
2Department of Statistics, St. Xaviers College (Autonomous), Mumbai, India
*

Corresponding author. Email: ullllhasdixit@yahoo.com.in

Received 10 March 2017, Accepted 27 December 2017, Available Online 31 December 2018.
DOI
10.2991/jsta.2018.17.4.6How to use a DOI?
Keywords
Multivariate geometric distribution; Maximum likelihood estimator; Uniformly minimum variance unbiased estimator; modified MLE
Abstract

The maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) for the parameters of a multivariate geometric distribution (MGD) have been derived. A modification of the MLE estimator (modified MLE) has been derivedin which case the bias is reduced. The mean square error (MSE) of the modified MLE is less than the MSE of the MLE. Variances of the parameters and the corresponding generalized variance (GV) has been obtained. It has been shown that the MLE and modified MLE are consistent estimators. A comparison of the GVs of modified MLE and UMVUE has shown that the modified MLE is more efficient than the UMVUE. In the final section its application has been discussed with an example of actual data.

Copyright
© 2018 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

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<Previous Article In Issue
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Journal
Journal of Statistical Theory and Applications
Volume-Issue
17 - 4
Pages
636 - 646
Publication Date
2018/12/31
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.2018.17.4.6How to use a DOI?
Copyright
© 2018 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - U. J. Dixit
AU  - S. Annapurna
PY  - 2018
DA  - 2018/12/31
TI  - Efficient Estimator of Parameters of a Multivariate Geometric Distribution
JO  - Journal of Statistical Theory and Applications
SP  - 636
EP  - 646
VL  - 17
IS  - 4
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2018.17.4.6
DO  - 10.2991/jsta.2018.17.4.6
ID  - Dixit2018
ER  -