Recent advances in estimation techniques have underscored the growing importance of shrinkage estimation and balanced loss functions in the analysis of multivariate normal distributions. These ...

In this paper the multivariate skew normal distribution, introduced by Azzalini and Dalla Valle (1996), is used as a basis in density expansions. A short summary of main properties of the distribution ...

1. Aspects of multivariate analysis -- 2. Matrix algebra and random vectors -- 3. Sample geometry and random sampling -- 4. The multivariate normal distribution -- 5. Inferences about a mean vector -- ...

Environmental data often include left-censored values reported to be less than some limit of detection (LOD). While simple imputation of a specific value such as LOD/2 is common, maximum likelihood ...

The normal distribution is a concept in statistics that assumes all values are distributed in the same pattern. It requires symmetry and consistent proportions in the distribution of values. Normal ...