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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

100%

Arora S., Mahajan K. K., Jangra V.

Statistics in Transition new series

2022

vol. 23

issue 2

49-68

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.

Bayesian estimation of fertility rates under imperfect age reporting

88%

Verma V., Nath D. C., Dwivedi S. N.

Statistics in Transition new series

2023

vol. 24

issue 2

39-57

This article outlines the application of the Bayesian method of parameter estimation to situations where the probability of age misreporting is high, leading to transfers of an individual from one age group to another. An essential requirement for Bayesian estimation is prior distribution, derived for both perfect and imperfect age reporting. As an alternative to the Bayesian methodology, a classical estimator based on the maximum likelihood principle has also been discussed. Here, the age misreporting probability matrix has been constructed using a performance indicator, which incorporates the relative performance of estimators based on age when reported correctly instead of misreporting. The initial guess of performance indicators can either be empirically or theoretically derived. The method has been illustrated by using data on Empowered Action Group (EAG) states of India from National Family Health Survey-3 (2005-2006) to estimate the total marital fertility rates. The present study reveals through both a simulation and real-life set-up that the Bayesian estimation method has been more promising and reliable in estimating fertility rates, even in situations where age misreporting is higher than in case of classical maximum likelihood estimates.

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2 Statistics in Transition new series

1 Arora S.

1 Dwivedi S. N.

1 Jangra V.

1 Mahajan K. K.

1 Nath D. C.

1 Verma V.

1 2023

1 2022

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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

Bayesian estimation of fertility rates under imperfect age reporting