The customary use of the normal model is seriously questioned when the population distribution is symmetric but have heavier tails than the normal distribution. Also, the normal model fails to incorporate dependent but uncorrelated responses. In such cases the multivariate Student-t distribution provides an appropriate model for the population. Such a model can be viewed as a mixture of normal and inverted gamma distributions. Using this result we have obtained the maximum likelihood estimators of the mean and scale parameters of multivariate Student-t distribution. The model has been used to find appropriate test statistic to test the mean vector. The non-null distribution of the test statistic has been derived. The distribution of the sum of squares and product matrix for the multivariate Student-t model as well as the predictive distribution of future model have been proposed. Similar results for the matrix T and elliptical models are also obtained. This project will extend this work.

Professor Shahjahan Khan

• School of Agricultural and Environmental Sciences

• Other Medical and Health Sciences
• Statistics

• Doctor of Philosophy (DPHD)
• Master of Research (MRES)