Test of fit for Marshall–Olkin distributions with applications

Meintanis, Simos G.

doi:10.1016/j.jspi.2007.04.013

Cited by 108 publications

(73 citation statements)

References 11 publications

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“…We have also constructed the asymptotic confidence intervals using the idea of Louis [11] and it is observed that even for moderate sample sizes the asymptotic results can be used for constructing confidence intervals and hence for testing purposes also. We have re-analyzed one data set, which was originally analyzed by Meintanis [15] using MOBE distribution, and we observed that for that data set MOBW model provides a better fit than the bivariate exponential model.…”

Section: Discussionmentioning

confidence: 99%

“…For illustrative purpose, in this section we have analyzed one data set from Meintanis [15] and it is presented in …”

Section: Discussionmentioning

confidence: 99%

“…Meintanis [15] analyzed this data by using MOBE distribution. We would like to analyze the data using MOBW model also.…”

Section: Discussionmentioning

confidence: 99%

“…We have also computed 95% confidence intervals of α, λ 0 , λ 1 , λ 2 using the observed Fisher information matrix obtained from the EM algorithm (presented in the appendix) as suggested by Louis [11] and they are as follows; (1. Now from the confidence interval of α, from the log-likelihood values and also from the Kolmogorov-Smirnov distances, it is clear that although Meintanis [15] suggested to use MOBE, MOBW is preferable in this case.…”

Section: Discussionmentioning

confidence: 99%

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Estimating the parameters of the Marshall–Olkin bivariate Weibull distribution by EM algorithm

Kundu

Dey

2009

Computational Statistics & Data Analysis

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In this paper we consider the Marshall-Olkin bivariate Weibull distribution. The Marshall-Olkin bivariate Weibull distribution is a singular distribution, whose both the marginals are univariate Weibull distributions. This is a generalization of the Marshall-Olkin bivariate exponential distribution. The cumulative joint distribution of the Marshall-Olkin bivariate Weibull distribution is a mixture of an absolute continuous distribution function and a singular distribution function. This distribution has four unknown parameters and it is observed that the maximum likelihood estimators of the unknown parameters can not be obtained in explicit forms. In this paper we discuss about the computation of the maximum likelihood estimators of the unknown parameters using EM algorithm. We perform some simulations to see the performances of the EM algorithm and re-analyze one data set for illustrative purpose.

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Section: Discussionmentioning

confidence: 99%

“…For illustrative purpose, in this section we have analyzed one data set from Meintanis [15] and it is presented in …”

Section: Discussionmentioning

confidence: 99%

“…Meintanis [15] analyzed this data by using MOBE distribution. We would like to analyze the data using MOBW model also.…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Estimating the parameters of the Marshall–Olkin bivariate Weibull distribution by EM algorithm

Kundu

Dey

2009

Computational Statistics & Data Analysis

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“…Next we analyse the soccer data for the years 2004-05 and 2005-06 which was studied by Meintanis (2007). Kundu and Gupta (2009) have fitted BVGE distribution and bivariate Marshall-Olkin (1967) distribution to this data.…”

Section: Discussionmentioning

confidence: 99%

An EM algorithm for the estimation of parameters of bivariate generalized exponential distribution under random left censoring

Dewan

Nandi

2013

Journal of Statistical Computation and Simulation

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Inference for dependence competing risks with partially observed failure causes from bivariate Gompertz distribution under generalized progressive hybrid censoring

Wang

Tripathi

Dey³

et al. 2020

Quality & Reliability Eng

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Competing risks model is considered with dependence causes of failure in this paper. When the latent failure times are distributed by a bivariate Gompertz model, statistical inference for the unknown model parameters is studied from classical and Bayesian approaches, respectively. Under a generalized progressive hybrid censoring, maximum likelihood estimators of the unknown parameters together with the associated existence and uniqueness are established, and the approximate confidence intervals are also obtained based on asymptotic likelihood theory via the observed Fisher information matrix. Moreover, Bayes estimates and the highest posterior density credible intervals of the unknown parameters are also provided based on a flexible Gamma–Dirichlet prior, and Monte Carlo sampling method is also derived to compute associated estimates. Finally, simulation studies and a real‐life example are given for illustration purposes.

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Test of fit for Marshall–Olkin distributions with applications

Cited by 108 publications

References 11 publications

Estimating the parameters of the Marshall–Olkin bivariate Weibull distribution by EM algorithm

Estimating the parameters of the Marshall–Olkin bivariate Weibull distribution by EM algorithm

An EM algorithm for the estimation of parameters of bivariate generalized exponential distribution under random left censoring

Inference for dependence competing risks with partially observed failure causes from bivariate Gompertz distribution under generalized progressive hybrid censoring

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