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Mathematical Biosciences and Engineering

2021, Volume 18, Issue 3: 2930-2951. doi: 10.3934/mbe.2021148
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Bayesian and maximum likelihood estimations of the Dagum parameters under combined-unified hybrid censoring

  • Department of Statistics and Operations Research, College of Science, King Saud University, P.O.Box 2455, Riyadh 11451, Saudi Arabia
  • Received: 28 January 2021 Accepted: 17 March 2021 Published: 29 March 2021

  • In this paper, we introduce a new form of hybrid censoring sample, that is called COMBINED-UNIFIED (C-U) hybrid sample. In this unified approach, we merge the combined hybrid censoring sampling that considered by Huang and Yang [1] and unified hybrid censoring sampling that considered by Balakrishnan et al. [2]. We apply the C-U hybrid censoring sampling to develop estimation procedures of the unknown parameters of Dagum distribution. The maximum likelihood method is used to estimate the unknown parameters and the asymptotic confidence intervals as well as the bootstrap confidence intervals are obtained. Also, we develop the Bayesian estimation of the unknown parameters of Dagum distribution under the squared error and linear-exponential (LINEX) loss functions. Since the closed forms of the Bayesian estimators are not available, so we encounter some computational difficulties to evaluate the Bayes estimates of the parameters involved in the model such as Tierney and Kadanes procedure as well as Markov Chain Monte Carlo (MCMC) procedure to compute approximate Bayes estimates. In addition, we show the usefulness of the theoretical findings thought some simulation experiments. Finally, a real data set have been analyzed for illustrative purposes of our results

    Citation: Walid Emam, Khalaf S. Sultan. Bayesian and maximum likelihood estimations of the Dagum parameters under combined-unified hybrid censoring[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2930-2951. doi: 10.3934/mbe.2021148

    Related Papers:

  • In this paper, we introduce a new form of hybrid censoring sample, that is called COMBINED-UNIFIED (C-U) hybrid sample. In this unified approach, we merge the combined hybrid censoring sampling that considered by Huang and Yang [1] and unified hybrid censoring sampling that considered by Balakrishnan et al. [2]. We apply the C-U hybrid censoring sampling to develop estimation procedures of the unknown parameters of Dagum distribution. The maximum likelihood method is used to estimate the unknown parameters and the asymptotic confidence intervals as well as the bootstrap confidence intervals are obtained. Also, we develop the Bayesian estimation of the unknown parameters of Dagum distribution under the squared error and linear-exponential (LINEX) loss functions. Since the closed forms of the Bayesian estimators are not available, so we encounter some computational difficulties to evaluate the Bayes estimates of the parameters involved in the model such as Tierney and Kadanes procedure as well as Markov Chain Monte Carlo (MCMC) procedure to compute approximate Bayes estimates. In addition, we show the usefulness of the theoretical findings thought some simulation experiments. Finally, a real data set have been analyzed for illustrative purposes of our results


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