References
1. Pearson, K. Contributions to the mathematical theory
of evolution. II. Skew variation in homogeneous
material", Philosophical Transactions of the Royal
Society of London, 186(Part I), pp. 343{424 (1895).
2. Kendall, M. and Stuart, A., The Advanced Theory of
Statistics, 4th Ed., 1, Distribution Theory, London:
Grin (1977).
3. Firat, M., Koc, A.C., Dikbas, F., et al. Identi cation
of homogeneous regions and regional frequency analysis
for Turkey", Scientia Iranica, Transactions A, Civil
Engineering, 21(5), pp. 1492{1502 (2014).
4. Harvey, A. and Sucarrat, G. EGARCH models
with fat tails, skewness and leverage", Computational
Statistics & Data Analysis, 76, pp. 320{338 (2014).
5. Amaya, D., Christo ersen, P., Jacobs, K., et al. Does
realized skewness predict the cross-section of equity
returns?", Journal of Financial Economics, 118(1),
pp. 135{167 (2015).
6. Astebro, T., Mata, J., and Santos-Pinto, L. Skewness
seeking: risk loving, optimism or overweighting of
small probabilities?", Theory and Decision, 78(2), pp.
189{208 (2015).
7. Ho, A.D. and Yu, C.C. Descriptive statistics for
modern test score distributions: Skewness, kurtosis,
discreteness, and ceiling e ects", Educational and
Psychological Measurement, 75(3), pp. 365{388 (2015).
8. Decker, R.A., Haltiwanger, J., Jarmin, R.S., et al.
Where has all the skewness gone? The decline in highgrowth
(young) rms in the US", European Economic
Review, 86, pp. 4{23 (2016).
9. Colacito, R., Ghysels, E., Meng, J., et al. Skewness in
expected macro fundamentals and the predictability of
equity returns: Evidence and theory", The Review of
Financial Studies, 29(8), pp. 2069{2109 (2016).
10. Ensthaler, L., Nottmeyer, O., Weizsacker, G., et al.
Hidden skewness: On the diculty of multiplicative
compounding under random shocks", Management
Science, 64(4), pp. 1693{1706 (2017).
A.A. Khan et al./Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 3525{3537 3537
11. Amjadzadeh, M. and Ansari-Asl, K. An innovative
emotion assessment using physiological signals based
on the combination mechanism", Scientia Iranica,
24(6), pp. 3157{3170 (2017).
12. Taylor, S. and Fang, M. Unbiased weighted variance
and skewness estimators for overlapping returns",
Swiss Journal of Economics and Statistics, 154(1), pp.
1{8 (2018).
13. Zwet, W.R., Convex Transformations of Random Variables,
Mathematisch Centrum, Amsterdam (1964).
14. Goldstein, J.L., Schrott, H.G., Hazzard, W.R., et al.
Hyperlipidemia in coronary heart disease II. Genetic
analysis of lipid levels in 176 families and delineation
of a new inherited disorder, combined hyperlipidemia",
The Journal of Clinical Investigation, 52(7), pp. 1544{
1568 (1973).
15. Mardia, K.V., Families of Bivariate Distributions, 27,
Lubrecht & Cramer Ltd (1970).
16. Aucremanne, L., Brys, G., Hubert, M., et al. A
study of Belgian in
ation, relative prices and nominal
rigidities using new robust measures of skewness and
tail weight", Statistics for Industry and Technology,
pp. 13{25 (2004).
17. Brys, G., Hubert, M., and Struyf, A. A robust
measure of skewness", Journal of Computational and
Graphical Statistics, 13(4), pp. 996{1017 (2004).
18. Doane, D.P. and Seward, L.E. Measuring skewness: a
forgotten statistic?", Journal of Statistics Education,
19(2), pp. 1{18 (2011).
19. Hosking, J. Moments or L moments? An example
comparing two measures of distributional shape", The
American Statistician, 46(3), pp. 186{189 (1992).
20. Li, X., Qin, Z., and Kar, S. Mean-variance-skewness
model for portfolio selection with fuzzy returns", European
Journal of Operational Research, 202(1), pp.
239{247 (2010).
21. Arnold, B.C. and Groeneveld, R.A. Measuring skewness
with respect to the mode", The American Statistician,
49(1), pp. 34{38 (1995).
22. Brys, G., Hubert, M., and Struyf, A. A comparison
of some new measures of skewness", Developments
in Robust Statistics (ICORS 2001), 14, pp. 98{113
(2003).
23. Kim, T.H. and White, H. On more robust estimation
of skewness and kurtosis", Finance Research Letters,
1(1), pp. 56{73 (2004).
24. Holgersson, H. A modi ed skewness measure for
testing asymmetry", Communications in Statistics-
Simulation and Computation, 39(2), pp. 335{346
(2010).
25. Tajuddin, I. On the use of medcouple as a measure of
skewness", Pakistan Journal of Statistics, 28(1), pp.
69{80 (2012).
26. Altinay, G. A simple class of measures of skewness",
MPRA Paper No. 72353, posted 4 July 2016,
https://mpra.ub.uni-muenchen.de/72353/(2016).
27. Oja, H. On location, scale, skewness and kurtosis
of univariate distributions", Scandinavian Journal of
Statistics, 8(3), pp. 154{168 (1981).