Efficient Estimator of Parameters of a Multivariate Geometric Distribution

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 derived in which case the bias is reduced. The mean square...

Full description

Saved in:
Bibliographic Details
Published inJournal of statistical theory and applications Vol. 17; no. 4; pp. 636 - 646
Main Authors Dixit, U. J., Annapurna, S.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 2018
Subjects
Research Article
Maximum likelihood estimator
modified MLE
Uniformly minimum variance unbiased estimator
Multivariate geometric distribution
62F10
Online AccessGet full text

Cover

More Information
Summary: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 derived in 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.
ISSN:1538-7887
2214-1766
DOI:10.2991/jsta.2018.17.4