Parameter estimation in multivariate analysis is important, particularly when parameter space is restricted. Among different methods, the shrinkage estimation is of interest. In this article we consider the problem of estimating the p-dimensional mean vector in spherically symmetric models. A dominant class of Baranchik-type shrinkage estimators is developed that outperforms the natural estimator under the balance loss function, when the mean vector is restricted to lie in a non-negative hyperplane. In our study, the components of the diagonal covariance matrix are assumed to be unknown. The performance evaluation of the proposed class of estimators is checked through a simulation study along with a real data analysis.

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In this paper, A new class of distributions called the Zografos-Balakrishnan odd log-logistic Generalized halfnormal (ZOLL-GHN) family with four parameters is introduced and studied. Useful representations and some mathematical properties of the new family include moments, quantile function, moment Generating function are investigated. The maximum likelihood equations for estimating the parameters based on real data are given. Different methods have been used to estimate its parameters such as maximum likelihood, Least squares, weighted least squares, Crammer-von-Misers, Anderson-Darling and right-tailed Anderson-Darling methods. We assesses the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study. Finally, the usefulness of the family and fitness capability of this model, are illustrated by means of two real data sets.