Estimation of inequality indices based on ranked set sampling

N. Nakhaei Rad; G. R. Mohtashami Borzadaran; H. Yari

Research Article

Year 2018, Volume: 47 Issue: 3, 709 - 720, 01.06.2018

N. Nakhaei Rad G. R. Mohtashami Borzadaran , H. Yari

Abstract

References

A.B. Atkinson, On the measurement of inequality. Journal of Economic Theory, 2(1970), pp. 244-263.
C. Kleiber and S. Kotz, Statistical Size Distributions in Economics and Actuarial Sciences, Wiely, New York, 2003.
F.A. Cowell and K. Kugo, Additivity and entropy concept: An axiomatic approach to in- equality measurement, Journal of Economic Theory, 25 (1981), pp. 131-143.
F.A. Cowell and E. Flachaire, Income distribution and inequality measurement: The prob- lem of extreme values. Journal of Econometrics, (2007), doi:10.1016/j.jeconom.2007.01.001.
G.A. McIntyre, A method for unbiased selective sampling, using ranked sets, Australian Lournal of Agricultural Research. 2 (1952), pp. 385-390.
G.P. Patil, A.K. Sinha and C. Taillie, Ranked set sampling from a nite population in the presence of a trend on a site, Journal of Applied Statistical Science, 1(1993), pp. 51-65.
G.P. Patil, A.K. Sinha and C. Taillie, Relative precision of ranked set sampling: a compar- ison with the regression estimator. Environmetrics, 4(1993), pp. 399-412.
J.B. McDonald and M. Ransom, The generalized beta distribution as a model for the distri- bution of income: estimation of related measure of inequality, Economic Studies in Equality, Social Exclusion and Well-Being, 5 (2008), pp. 147-166.
K. Takahashi and K. Wakimoto, On unbiased estimates of the population mean based on the sample stratied by mean of ordering, Annals of the Institute of Statistical Mathematics, 20 (1968), pp. 1-31.
M.M. Al-Talib and A.D. Al-Nasser, Estimation of Gini index from continuous distrib-ution based on ranked set sampling, Electronic Journal of Applied Statistical Analysis. 1 (2008) , pp. 33-41.
N.N. Chuiv and B.K. Sinha, On some aspects of ranked set sampling in parametric esti- mation. In: Handbook of Statistics, Vol. 17, N. Balakrishnan and C.R. Rao, Eds., Elsevier, Amesterdam, 1998. pp. 337-377.
P. Bansal, S. Arora, and K. Mahajan, Estimation of inequality indices based on simple random ranked set and systematic sampling, ISRN Probability and Statistics, Article ID: 659580 (2013).
R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. ISBN 3-900051-07-0, URL http://www.R-project.org/.
S.L. Stokes, Ranked set sampling with concomitant variables, Comm. Statist. Theory Meth- ods, 6 (1977), pp. 1207-1211.
S.L. Stokes, Estimation of variance using judgment ordered ranked set samples, Biometrics, 36 (1980), pp. 35-42.
S.L. Stokes, Parametric ranked set sampling, Ann. Inst. Statist. Math, 47 (1995), pp. 465- 482.
S.L. Stokes and T.W. Sager, Characterization of a ranked-set sample with application to estimating distribution functions, J. Amer. Statist. Assoc., 83 (1988), pp. 35-42.
T.R. Dell and J.L. Clutter, Ranked set sampling theory with order statistics background, Biometrica, 28 (1972), pp. 545-553.

Estimation of inequality indices based on ranked set sampling

Year 2018, Volume: 47 Issue: 3, 709 - 720, 01.06.2018

N. Nakhaei Rad G. R. Mohtashami Borzadaran , H. Yari

Abstract

Measuring the income inequality is a major concern of the economists. Therefore, numerous indices have been devised to show different features of the income inequality. In general, the simple random sampling procedure is commonly utilized to estimate the inequality measures, while the ranked set sampling is a more cost saving method which increases the precision and the efficiency of the inequality estimators. In this paper the advantages of the ranked set sampling when measuring the amount of the income inequality are examined. Through using Monte Carlo simulation technique, this paper proves that the ranked set sampling, increases the precision of inequality indices estimations. In the end, a real income data set is analyzed to illustrate the obtained results.

Keywords

Ranked set sampling, Gini index, Theil index, MLD index, Atkinson index, Monte Carlo simulation, Generalized beta distribution of the first kind, Generalized beta distribution of the second kind, Generalized gamma distribution

References

A.B. Atkinson, On the measurement of inequality. Journal of Economic Theory, 2(1970), pp. 244-263.
C. Kleiber and S. Kotz, Statistical Size Distributions in Economics and Actuarial Sciences, Wiely, New York, 2003.
F.A. Cowell and K. Kugo, Additivity and entropy concept: An axiomatic approach to in- equality measurement, Journal of Economic Theory, 25 (1981), pp. 131-143.
F.A. Cowell and E. Flachaire, Income distribution and inequality measurement: The prob- lem of extreme values. Journal of Econometrics, (2007), doi:10.1016/j.jeconom.2007.01.001.
G.A. McIntyre, A method for unbiased selective sampling, using ranked sets, Australian Lournal of Agricultural Research. 2 (1952), pp. 385-390.
G.P. Patil, A.K. Sinha and C. Taillie, Ranked set sampling from a nite population in the presence of a trend on a site, Journal of Applied Statistical Science, 1(1993), pp. 51-65.
G.P. Patil, A.K. Sinha and C. Taillie, Relative precision of ranked set sampling: a compar- ison with the regression estimator. Environmetrics, 4(1993), pp. 399-412.
J.B. McDonald and M. Ransom, The generalized beta distribution as a model for the distri- bution of income: estimation of related measure of inequality, Economic Studies in Equality, Social Exclusion and Well-Being, 5 (2008), pp. 147-166.
K. Takahashi and K. Wakimoto, On unbiased estimates of the population mean based on the sample stratied by mean of ordering, Annals of the Institute of Statistical Mathematics, 20 (1968), pp. 1-31.
M.M. Al-Talib and A.D. Al-Nasser, Estimation of Gini index from continuous distrib-ution based on ranked set sampling, Electronic Journal of Applied Statistical Analysis. 1 (2008) , pp. 33-41.
N.N. Chuiv and B.K. Sinha, On some aspects of ranked set sampling in parametric esti- mation. In: Handbook of Statistics, Vol. 17, N. Balakrishnan and C.R. Rao, Eds., Elsevier, Amesterdam, 1998. pp. 337-377.
P. Bansal, S. Arora, and K. Mahajan, Estimation of inequality indices based on simple random ranked set and systematic sampling, ISRN Probability and Statistics, Article ID: 659580 (2013).
R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2012. ISBN 3-900051-07-0, URL http://www.R-project.org/.
S.L. Stokes, Ranked set sampling with concomitant variables, Comm. Statist. Theory Meth- ods, 6 (1977), pp. 1207-1211.
S.L. Stokes, Estimation of variance using judgment ordered ranked set samples, Biometrics, 36 (1980), pp. 35-42.
S.L. Stokes, Parametric ranked set sampling, Ann. Inst. Statist. Math, 47 (1995), pp. 465- 482.
S.L. Stokes and T.W. Sager, Characterization of a ranked-set sample with application to estimating distribution functions, J. Amer. Statist. Assoc., 83 (1988), pp. 35-42.
T.R. Dell and J.L. Clutter, Ranked set sampling theory with order statistics background, Biometrica, 28 (1972), pp. 545-553.

There are 18 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Statistics
Authors	N. Nakhaei Rad This is me G. R. Mohtashami Borzadaran H. Yari This is me
Publication Date	June 1, 2018
Published in Issue	Year 2018 Volume: 47 Issue: 3

Cite

APA	Rad, N. N., Mohtashami Borzadaran, G. R., & Yari, H. (2018). Estimation of inequality indices based on ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 47(3), 709-720.
AMA	Rad NN, Mohtashami Borzadaran GR, Yari H. Estimation of inequality indices based on ranked set sampling. Hacettepe Journal of Mathematics and Statistics. June 2018;47(3):709-720.
Chicago	Rad, N. Nakhaei, G. R. Mohtashami Borzadaran, and H. Yari. “Estimation of Inequality Indices Based on Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 47, no. 3 (June 2018): 709-20.
EndNote	Rad NN, Mohtashami Borzadaran GR, Yari H (June 1, 2018) Estimation of inequality indices based on ranked set sampling. Hacettepe Journal of Mathematics and Statistics 47 3 709–720.
IEEE	N. N. Rad, G. R. Mohtashami Borzadaran, and H. Yari, “Estimation of inequality indices based on ranked set sampling”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, pp. 709–720, 2018.
ISNAD	Rad, N. Nakhaei et al. “Estimation of Inequality Indices Based on Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 47/3 (June 2018), 709-720.
JAMA	Rad NN, Mohtashami Borzadaran GR, Yari H. Estimation of inequality indices based on ranked set sampling. Hacettepe Journal of Mathematics and Statistics. 2018;47:709–720.
MLA	Rad, N. Nakhaei et al. “Estimation of Inequality Indices Based on Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, 2018, pp. 709-20.
Vancouver	Rad NN, Mohtashami Borzadaran GR, Yari H. Estimation of inequality indices based on ranked set sampling. Hacettepe Journal of Mathematics and Statistics. 2018;47(3):709-20.