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A Bayesian estimation of the Gini index and the Bonferroni index for the Dagum distribution with the application of different priors

Author

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  • Arora Sangeeta

    (Department of Statistics, Panjab University, Chandigarh, India .)

  • Mahajan Kalpana K.

    (Department of Statistics, Panjab University, Chandigarh, India .)

  • Jangra Vikas

    (Department of Statistics, Panjab University, Chandigarh, India .)

Abstract

Bayesian estimators and highest posterior density credible intervals are obtained for two popular inequality measures, viz. the Gini index and the Bonferroni index in the case of the Dagum distribution. The study considers informative and non-informative priors, i.e. the Mukherjee-Islam prior and the extension of Jeffrey’s prior, respectively, under the presumption of the Linear Exponential (LINEX) loss function. A Monte Carlo simulation study is carried out in order to obtain the relative efficiency of both the Gini and Bonferroni indices while taking into consideration different priors and loss functions. The estimated loss proves lower when using the Mukherjee-Islam prior in comparison to the extension of Jeffrey’s prior and the LINEX loss function outperforms the squared error loss function (SELF) in terms of the estimated loss. Highest posterior density credible intervals are also obtained for both these measures. The study used real-life data sets for illustration purposes.

Suggested Citation

  • Arora Sangeeta & Mahajan Kalpana K. & Jangra Vikas, 2022. "A Bayesian estimation of the Gini index and the Bonferroni index for the Dagum distribution with the application of different priors," Statistics in Transition New Series, Polish Statistical Association, vol. 23(2), pages 49-68, June.
    • Handle: RePEc:vrs:stintr:v:23:y:2022:i:2:p:49-68:n:10
    DOI: 10.2478/stattrans-2022-0016
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