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313810

On Estimating the Parameters of the Bivariate Normal Distribution

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Last updated: 28 Dec 2024

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Abstract

A technique is applied to estimate the parameters of the bivariate normal distribution with unknown mean vector and unknown covariance matrix by minimizing the Cramer von Mises distance from a non-parametric density estimate and the parametric estimate at the order statistics. The maximum likelihood estimators were found and a comparison was made with the proposed estimator. For different parameters of the true density the proposed estimators were tested using a Monte Carlo experiment. The results show an improvement in mean integrated square error which is taken as a measure of the closeness of the estimated density and the true density.  

DOI

10.21608/esju.2001.313810

Keywords

The Bivariate Normal Distribution, The Cramer Von Mises Distance, Maximum likelihood, Monte Carlo

Volume

45

Article Issue

2

Related Issue

43029

Issue Date

2001-12-01

Publish Date

2001-12-01

Page Start

143

Page End

154

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_313810.html

Detail API

https://esju.journals.ekb.eg/service?article_code=313810

Order

2

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

On Estimating the Parameters of the Bivariate Normal Distribution

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Article

Created At

28 Dec 2024