A Bivariate Geometric Distribution with Applications to Reliability

Krishna, Hare; Pundir, Pramendra Singh

doi:10.1080/03610920802364096

Cited by 21 publications

(9 citation statements)

References 2 publications

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“…Similarly it is possible to obtain UMVUE for various combinations of p a 1 1 p a 2 2 p a 3 3 for different values of a 1 ,a 2 ,a 3 ,b 1 ,b 2 and b 3 .…”

Section: Uniform Minimum Variance Unbiased Estimator (Umvue)mentioning

confidence: 99%

“…On the same lines, Gultekin and Bairamov [7] constructed a trivariate geometric distribution and the corresponding multivariate extension. Srivastava and Bagchi [8] introduced the multivariate version of a geometric distribution and obtained certaincharacterizations.Vasudeva and Srilakshminarayana [9] established some properties of the MGD and also obtained a characterization assuming it to follow the power series distribution.…”

Section: Introductionmentioning

confidence: 96%

“…Hare Krishna and Pundir [3] have obtained the MLE and Bayes estimators of the parameters for this BGD. Dixit and Annapurna [4] have further obtained the UMVUE estimators and have compared the MLE and UMVUE based on the (MSEs).…”

Section: Introductionmentioning

confidence: 99%

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Efficient Estimator of Parameters of a Multivariate Geometric Distribution

Dixit¹,

Annapurna²

2018

JSTA

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A B S T R A C TThe 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.This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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“…Similarly it is possible to obtain UMVUE for various combinations of p a 1 1 p a 2 2 p a 3 3 for different values of a 1 ,a 2 ,a 3 ,b 1 ,b 2 and b 3 .…”

Section: Uniform Minimum Variance Unbiased Estimator (Umvue)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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Efficient Estimator of Parameters of a Multivariate Geometric Distribution

Dixit¹,

Annapurna²

2018

JSTA

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“…This distribution allows also for negative correlations and comprises the product of two independent geometrics as a special case. Phatak and Sreehari (1981) introduced a two-parameter bivariate geometric distribution with an easy expression of its p.m.f., allowing for positive correlations only; it was also studied later by Krishna and Pundir (2009). Roy (1993) extended the univariate concept of failure rate for non-negative integer valued discrete variables in two dimensions, by introducing a new definition of bivariate failure rates, and proposed a three-parameter bivariate geometric distribution enjoying an analogous property to its univariate version, i.e., locally constant bivariate failure rates.…”

Section: Introductionmentioning

confidence: 99%

A bivariate geometric distribution allowing for positive or negative correlation

Barbiero

2018

Communications in Statistics - Theory and Methods

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In this paper, we propose a new bivariate geometric model, derived by linking two univariate geometric distributions through a specific copula function, allowing for positive and negative correlations. Some properties of this joint distribution are presented and discussed, with particular reference to attainable correlations, conditional distributions, reliability concepts, and parameter estimation. A Monte Carlo simulation study empirically evaluates and compares the performance of the proposed estimators in terms of bias and standard error. Finally, in order to demonstrate its usefulness, the model is applied to a real data set.

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“…The joint probability mass function of (X,Y) is given by Kocherlakote (1992) ; otherwise (1.1) Krishna and Pundir(2009) estimated the parameters of BGD as given in (1.1). Krishna and Pundir(2009) have derived MLE of the parameters and the reliability functions. Further they have derived asymptotic expected values of MLE and reliability functions.But they have not obtained the UMVUE of the parameters of the BGD.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Parameters of a Bivariate Geometric Distribution

Dixit¹,

Annapurna²

2015

JSTA

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The uniformly minimum variance unbiased estimators (UMVUE) of the parameters and reliability functions of a bivariate geometric distribution(BGD) have been derived.The exact variances of the maximum likelihood estimator (MLE) and of UMVUE have been derived and the corresponding mean square errors have been compared.It is found that in some cases UMVUE is better and in some cases MLE is better with respect to the mean square errors. In the final section an example of actual data from the game Cricket's Indian Premium League 2014 (IPL 2014) has been given.

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A Bivariate Geometric Distribution with Applications to Reliability

Cited by 21 publications

References 2 publications

Efficient Estimator of Parameters of a Multivariate Geometric Distribution

Efficient Estimator of Parameters of a Multivariate Geometric Distribution

A bivariate geometric distribution allowing for positive or negative correlation

Estimation of the Parameters of a Bivariate Geometric Distribution

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