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A hierarchical model for the skew-normal distribution with application in developmental neurotoxicology. (English) Zbl 06302735

Summary: The distribution of the mean of a random sample drawn from a skew-normal population was derived by Chen et al. (2004). Here, we consider a hierarchical structure and derive the distribution of the sample mean when the location parameter itself is a random variable with a normal distribution. In neurotoxicological bioassay experiments with laboratory animals, often the response of interest is continuous in nature and the mean of responses is used for inferential purposes (Chen, 2006). However, in developmental neurotoxicity experiments where the neurological effect of a compound on the developing fetus is of interest, because of the intra-litter correlation, the mean of the response distribution may vary from one litter to another. The unconditional distribution of the litter sample mean is derived and its application in the analysis of data from developmental neurotoxicology is described. An example with real experimental data is used to provide further illustration.

MSC:

62-XX Statistics
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[1] DOI: 10.1016/j.jmva.2004.10.002 · Zbl 1073.62049 · doi:10.1016/j.jmva.2004.10.002
[2] DOI: 10.1214/08-BA320 · Zbl 1330.62242 · doi:10.1214/08-BA320
[3] DOI: 10.1016/j.jmva.2008.03.009 · Zbl 1151.62042 · doi:10.1016/j.jmva.2008.03.009
[4] DOI: 10.1007/BF02294652 · Zbl 0794.62075 · doi:10.1007/BF02294652
[5] Azzalini A., Statistica 46 pp 199– (1985) · Zbl 0964.62001
[6] DOI: 10.1111/j.1467-9469.2005.00426.x · Zbl 1091.62046 · doi:10.1111/j.1467-9469.2005.00426.x
[7] DOI: 10.1111/1467-9868.00194 · Zbl 0924.62050 · doi:10.1111/1467-9868.00194
[8] DOI: 10.1093/biomet/83.4.715 · Zbl 0885.62062 · doi:10.1093/biomet/83.4.715
[9] DOI: 10.1111/j.1539-6924.2005.00590.x · doi:10.1111/j.1539-6924.2005.00590.x
[10] DOI: 10.1080/03610920701713195 · Zbl 1135.62003 · doi:10.1080/03610920701713195
[11] Bayes C.L., Braz. J. Probab. Statist. 21 pp 141– (2007)
[12] Branco M.D., Scand. J. Statist.
[13] DOI: 10.2307/2533961 · Zbl 0885.62118 · doi:10.2307/2533961
[14] Chen J.J., Developmental and Reproductive Toxicology–A practical Approach, 2. ed. (2006)
[15] DOI: 10.1080/0094965031000147687 · Zbl 1060.62060 · doi:10.1080/0094965031000147687
[16] DOI: 10.1002/9780470481400 · Zbl 1180.91004 · doi:10.1002/9780470481400
[17] Dalla Valle A., Skew-Elliptical Distribution and Their Applications pp 1– (2004)
[18] DOI: 10.2307/2347446 · Zbl 0568.62067 · doi:10.2307/2347446
[19] DOI: 10.1016/j.csda.2005.12.002 · Zbl 1157.62533 · doi:10.1016/j.csda.2005.12.002
[20] Henze N., Scandinavian J. Statist. 13 pp 271– (1986)
[21] DOI: 10.1016/j.ntt.2007.06.001 · doi:10.1016/j.ntt.2007.06.001
[22] DOI: 10.1111/j.1539-6924.1993.tb01067.x · doi:10.1111/j.1539-6924.1993.tb01067.x
[23] Lin T.I., Statistica Sinica 17 pp 909– (2007)
[24] DOI: 10.2307/2532802 · Zbl 0825.62778 · doi:10.2307/2532802
[25] DOI: 10.1016/j.jspi.2004.06.062 · Zbl 1077.62017 · doi:10.1016/j.jspi.2004.06.062
[26] DOI: 10.1016/0378-4274(85)90044-X · doi:10.1016/0378-4274(85)90044-X
[27] Mohammad F.K., Neurobehav. Toxicol. Teratol. 8 pp 551– (1986)
[28] Organization for Economic Cooperation and Development (2003). OECD Environment, Health and Safety Publications Series on Testing and Assessment No. 20. Guidance Document for Neurotoxicity Testing. Environment Directorate, OECD, Paris.
[29] DOI: 10.1080/02664760050120542 · Zbl 1076.62514 · doi:10.1080/02664760050120542
[30] Razzaghi M., Staitistics for the Environment 4: Pollution Assessment and Control (1999)
[31] DOI: 10.1002/env.540 · doi:10.1002/env.540
[32] DOI: 10.1007/s10651-007-0072-6 · doi:10.1007/s10651-007-0072-6
[33] DOI: 10.1023/A:1009683114075 · doi:10.1023/A:1009683114075
[34] DOI: 10.1111/j.0272-4332.2004.00558.x · doi:10.1111/j.0272-4332.2004.00558.x
[35] DOI: 10.1016/j.jspi.2005.08.043 · Zbl 1098.62023 · doi:10.1016/j.jspi.2005.08.043
[36] SAS (2008). Statistical Analysis System 9.2, SAS Institute Inc., Cary, NC.
[37] Sidak Z., Theory of Rank Tests., 2. ed. (1999)
[38] DOI: 10.1111/j.1539-6924.1999.tb00420.x · doi:10.1111/j.1539-6924.1999.tb00420.x
[39] DOI: 10.2307/2529820 · Zbl 0333.62069 · doi:10.2307/2529820
[40] DOI: 10.1093/toxsci/66.2.298 · doi:10.1093/toxsci/66.2.298
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