Abstract
In this article, we consider classical and Bayesian estimations of some economic measures, specially Bonferroni Curve and Bonferroni Index of the Pareto distribution. We obtain the Maximum Likelihood Estimator and Uniform Minimum Variance Unbiased Estimator in the classical setup, and their properties are studied. Additionally, we conduct Bayesian estimation procedures based on symmetric loss functions and a truncated gamma prior. The precision of the estimators is evaluated under different sample sizes via Monte Carlo simulation. Furthermore, a real dataset is provided to compute all the estimators.
Acknowledgements
We sincerely appreciate the reviewers for dedicating their time to evaluate our manuscript. Their careful reading and insightful comments and suggestions have significantly enhanced the quality of this work.
References
[1] R. Aaberge, Characterizations of lorenz curves and income distributions, Social Choice Welfare 17 (2000), no. 4, 639–53. 10.1007/s003550000046Search in Google Scholar
[2] R. Aaberge, Ginis nuclear family, J. Econ. Inequality 5 (2007), no. 3, 305–322. 10.1007/s10888-006-9050-8Search in Google Scholar
[3] E. I. Abdul-Sathar, E. S. Jeevanand and K. R. Muraleedharan Nair, Bayesian estimation of Lorenz curve, Gini-index and variance of logarithms in a Pareto distribution, Statistica (Bologna) 65 (2005), no. 2, 193–205. Search in Google Scholar
[4] B. C. Arnold and S. J. Press, Bayesian inference for Pareto populations, J. Econometrics 21 (1983), no. 3, 287–306. 10.1016/0304-4076(83)90047-7Search in Google Scholar
[5] S. Arora, K. K. Mahajan and P. Godura, Bayesian estimation of Bonferroni curve and zenga curve in the case of dagum distribution, Recent Advances in Time Series Forecasting, Taylor & Francis, New York (2021), 51–77. 10.1201/9781003102281-4Search in Google Scholar
[6] N. Batir, Inequalities for the inverses of the polygamma functions, Arch. Math. (Basel) 110 (2018), no. 6, 581–589. 10.1007/s00013-018-1156-2Search in Google Scholar
[7] C. Bonferroni, Elmenti di statistica generale, Libreria Seber, Firenze, 1930. Search in Google Scholar
[8] S. R. Chakravarty, A deprivation-based axiomatic characterization of the absolute Bonferroni index of inequality, J. Econom. Theory 5 (2007), no. 3, 339–351. 10.1007/s10888-006-9054-4Search in Google Scholar
[9] M. Chandra and N. D. Singpurwalla, Relationships between some notions which are common to reliability theory and economics, Math. Oper. Res. 6 (1981), no. 1, 113–121. 10.1287/moor.6.1.113Search in Google Scholar
[10] M. Csörgő, J. L. Gastwirth and R. Zitikis, Asymptotic confidence bands for the Lorenz and Bonferroni curves based on the empirical Lorenz curve, J. Statist. Plann. Inference 74 (1998), no. 1, 65–91. 10.1016/S0378-3758(98)00103-7Search in Google Scholar
[11] D. Dyer, Structural probability bounds for the strong Pareto law, Canad. J. Statist. 9 (1981), no. 1, 71–77. 10.2307/3315297Search in Google Scholar
[12] G. M. Giorgi and M. Crescenzi, A look at the Bonferroni inequality measure in a reliability framework, Statistica (Bologna) 61 (2001), no. 4, 571–583. Search in Google Scholar
[13] G. M. Giorgi and M. Crescenzi, Bayesian estimation of the Bonferroni index from a Pareto-type I population, Stat. Methods Appl. 10 (2001), 41–48. 10.1007/BF02511638Search in Google Scholar
[14] G. M. Giorgi and R. Mondani, The exact sampling distribution of the Bonferroni concentration index, Metron 52 (1994), no. 3–4, 5–41. Search in Google Scholar
[15] G. M. Giorgi and R. Mondani, Sampling distribution of the Bonferroni inequality index from exponential population, Sankhyā Ser. B 57 (1995), no. 1, 10–18. Search in Google Scholar
[16] K. M. Hassanein and E. F. Brown, Estimation of bonferroni and total time on test curve using optimally selected order statistics in large samples, J. Statist. Res. 37 (2003), 31–42. Search in Google Scholar
[17] H. He, N. Zhou and R. Zhang, On estimation for the Pareto distribution, Stat. Methodol. 21 (2014), 49–58. 10.1016/j.stamet.2014.03.002Search in Google Scholar
[18] T. S. K. Moothathu, Sampling distributions of Lorenz curve and Gini index of the Pareto distribution, Sankhyā Ser. B 47 (1985), no. 2, 247–258. Search in Google Scholar
[19] T. S. K. Moothathu, The best estimator and a strongly consistent asymptotically normal unbiased estimator of Lorenz curve Gini index and Theil entropy index of Pareto distribution, Sankhyā Ser. B 52 (1990), no. 1, 115–127. Search in Google Scholar
[20] S. Pundir, S. Arora and K. Jain, Bonferroni curve and the related statistical inference, Statist. Probab. Lett. 75 (2005), no. 2, 140–150. 10.1016/j.spl.2005.05.024Search in Google Scholar
[21] K. V. Viswakala and E. I. Abdul Sathar, Classical estimation of hazard rate and mean residual life functions of Pareto distribution, Comm. Statist. Theory Methods 48 (2019), no. 17, 4367–4379. 10.1080/03610926.2018.1494289Search in Google Scholar
[22] J. Woo and G. Yoon, Estimations of Lorenz curve and Gini index in a pareto distribution, Comm. Statist. Appl. Methods 8 (2001), no. 1, 249–56. Search in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A Bayesian Extended Exponentially Weighted Moving Average Control Chart
- Assessment of Reliability of Power Systems Under Adverse Weather Condition Using Markov System Dynamic Method
- Time Truncated Attribute Median Control Charts for Logistic-Exponential Process Distribution
- Ageing Concepts for Bivariate Copulas
- Estimation of Bonferroni Curve and Bonferroni Index of the Pareto Distribution
Articles in the same Issue
- Frontmatter
- A Bayesian Extended Exponentially Weighted Moving Average Control Chart
- Assessment of Reliability of Power Systems Under Adverse Weather Condition Using Markov System Dynamic Method
- Time Truncated Attribute Median Control Charts for Logistic-Exponential Process Distribution
- Ageing Concepts for Bivariate Copulas
- Estimation of Bonferroni Curve and Bonferroni Index of the Pareto Distribution