並列摘要
The distribution of the mean of a random sample drawn from a skew-normal population was derived by Su and Gupta (2015). Here, we consider a hi- erarchical structure and derive the distribution of the sample mean when the location parameter itself is a random variable with a skew-normal dis- tribution. We propose a dose-response model for the data obtained from developmental neurotoxicological experiments. To account for the critical issue of the correlation among responses from pups in the same litter, the so called intralitter correlation, a hierarchical distributional structure is used to derive the underlying unconditional distribution of responses. The maximum likelihood method is used to estimate model parameters. An example with real experimental data is used to provide further illustration.
參考文獻
Arellano-Valle, R. B., and Genton, M. G. (2005). On fundamental skew
Azzalini, A. (2005). The Skew normal Distribution and Related Mul-
developmental toxicology. Handbook of statistics, 12, 507-533.
Liang, K. Y., and Hanfelt, J. (1994). On the use of the quasi-likelihood
method in teratological experiments. Biometrics, 872-880.