Abstract
In this paper, the desired sample size for estimating the skewness parameter with given closeness and confidence level under skew normal populations. The confidence intervals for skewness parameter are constructed based on the desired sample sizes using two pivots, chi-square distribution and F-distribution. Computer simulations support our main results. At the end, a real data example is provided for illustration of constructed confidence intervals.
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References
Azzalini, A.: A class of distributions which includes the normal ones. Scand. J. Stat. 12(2), 171–178 (1985)
Azzalini, A., Capitanio, A.: The Skew-Normal and Related Families, vol. 3. Cambridge University Press, Cambridge (2013)
Gupta, A.K., Chang, F.C.: Multivariate skew symmetric distributions. Appl. Math. Lett. 16, 643–646 (2003)
Gupta, A.K., Gouzalez, G., Dominguez-Molina, J.A.: A multivariate skew normal distribution. J. Multivariate Anal. 82, 181–190 (2004)
Gregoire, T., Affleck, D.: Estimating desired sample size for simple random sampling of a skewed population. Am. Stat. (2017). https://doi.org/10.1080/00031305.2017.1290548
Trafimow, D.: Using the coefficient of confidence to make the philosophical switch from a posteriori to a priori inferential statistics. Educ. Psychol. Measur. (2016)
Trafimow, D.: Using the coefficient of confidence to make the philosophical switch from a posteriori to a priori inferential statistics. Educ. Psychol. Measur. 77(5), 831–854 (2017)
Trafimow, D., MacDonald, J.A.: Performing inferential statistics prior to data collection. Educ. Psychol. Measur. 77(2), 204–219 (2017)
Trafimow, D., Wang, T., Wang, C.: From a sampling precision perspective, skewness is a friend and not an enemy! Educ. Psychol. Measur. 1–22 (2018). https://doi.org/10.1177/0013164418764801
Vernic, R.: Multivariate skew-normal distributions with applications in insurance. Insur. Math. Econ. 38, 413–426 (2006)
Wang, T., Li, B., Gupta, A.K.: Distribution of quadratic forms under skew normal settings. J. Multivariate Anal. 100, 533–545 (2009)
Ye, R., Wang, T.: Inferences in linear mixed models with skew-normal random effects. Acta Mathematica Sinica English Series 31(4), 576–594 (2015)
Zhu, X., Ma, Z., Wang, T., Teetranont, T.: Plausibility regions on the skewness parameter of skew normal distributions based on Inferential Models. In: Robustness in Econometrics. Studies in Computational Intelligence, vol. 692 (2017). https://doi.org/10.1007/978-3-319-50742-216
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Appendix 1
Appendix 1
The data set of the LAI obtained from June to October, 2010
Jun. | Jul. | Sep. | Oct. |
---|---|---|---|
4.87 | 3.32 | 2.05 | 1.50 |
5.00 | 3.02 | 2.12 | 1.46 |
4.72 | 3.28 | 2.24 | 1.55 |
5.16 | 3.63 | 2.56 | 1.27 |
5.11 | 3.68 | 2.67 | 1.26 |
5.03 | 3.79 | 2.61 | 1.37 |
5.36 | 3.68 | 2.42 | 1.87 |
5.17 | 4.06 | 2.58 | 1.75 |
5.56 | 4.13 | 2.56 | 1.81 |
4.48 | 2.92 | 1.84 | 1.98 |
4.55 | 3.05 | 1.94 | 1.89 |
4.69 | 3.02 | 1.95 | 1.71 |
2.54 | 2.78 | 2.29 | 1.29 |
3.09 | 2.35 | 1.94 | 1.34 |
2.79 | 2.40 | 2.20 | 1.29 |
3.80 | 3.28 | 1.56 | 1.10 |
3.61 | 3.45 | 1.40 | 1.04 |
3.53 | 2.85 | 1.36 | 1.08 |
2.51 | 3.05 | 1.60 | 0.86 |
2.41 | 2.78 | 1.50 | 0.70 |
2.80 | 2.72 | 1.88 | 0.82 |
3.23 | 2.64 | 1.63 | 1.19 |
3.46 | 2.88 | 1.66 | 1.24 |
3.12 | 3.00 | 1.62 | 1.14 |
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Wang, C., Wang, T., Trafimow, D., Myüz, H.A. (2019). Desired Sample Size for Estimating the Skewness Under Skew Normal Settings. In: Kreinovich, V., Sriboonchitta, S. (eds) Structural Changes and their Econometric Modeling. TES 2019. Studies in Computational Intelligence, vol 808. Springer, Cham. https://doi.org/10.1007/978-3-030-04263-9_11
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DOI: https://doi.org/10.1007/978-3-030-04263-9_11
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