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On uses of mean absolute deviation: decomposition, skewness and correlation coefficients

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  • Elsayed Amir

Abstract

The mean absolute deviation about mean is expressed as a covariance between a random variable and its under/over indicator functions. Based on this representation new correlation coefficients are derived. These correlation coefficients ensure high stability of statistical inference when we deal with distributions that are not symmetric and for which the normal distribution is not an appropriate approximation. The covariance representation of the mean absolute deviation allows obtaining a semi decomposition of Pietra’s index for income from different resources. Moreover, a measure of skewness based on the mean absolute deviation is discussed. By using simulation study it is shown that the mean absolute deviation correlation is outperforming the Pearson’s correlation for non-normal model. Copyright Sapienza Università di Roma 2012

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  • Elsayed Amir, 2012. "On uses of mean absolute deviation: decomposition, skewness and correlation coefficients," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 145-164, August.
    • Handle: RePEc:spr:metron:v:70:y:2012:i:2:p:145-164
    DOI: 10.1007/BF03321972
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    1. Magdalena Niewiadomska-Bugaj & Teresa Kowalczyk & Hend Ouda, 2006. "A new test of association and other tests based on the Gini mean difference," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 399-409.
    2. Lerman, Robert I. & Yitzhaki, Shlomo, 1989. "Improving the accuracy of estimates of Gini coefficients," Journal of Econometrics, Elsevier, vol. 42(1), pages 43-47, September.
    3. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    4. Muñoz-Perez, J. & Sanchez-Gomez, A., 1990. "A characterization of the distribution function: the dispersion function," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 235-239, August.
    5. Gastwirth, Joseph L, 1974. "Large Sample Theory of Some Measures of Income Inequality," Econometrica, Econometric Society, vol. 42(1), pages 191-196, January.
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    1. Postek, Krzysztof & Ben-Tal, A. & den Hertog, Dick & Melenberg, Bertrand, 2015. "Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information," Discussion Paper 2015-030, Tilburg University, Center for Economic Research.
    2. Postek, Krzysztof & Ben-Tal, A. & den Hertog, Dick & Melenberg, Bertrand, 2015. "Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information," Other publications TiSEM d718e419-a375-4707-b206-e, Tilburg University, School of Economics and Management.
    3. Wang, Yu & Zhang, Yu & Tang, Jiafu, 2019. "A distributionally robust optimization approach for surgery block allocation," European Journal of Operational Research, Elsevier, vol. 273(2), pages 740-753.

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