Test That Normal Mean Vector Lies In the Positive Orthant against the Negative One
 
                 
                
                    
                                        
                    - 
Graphical Abstract
 
                                        
                    - 
Abstract
    In the case of the independent random samples from n normal populations with a commonbut unknown variance, the likelihood ratio (LR) test that normal mean vector lies in the positiveorthant against the negative one is possible under mild conditions, and a new distribution, namedBeta Star distribution, which is found and used to determme the distribution of the LR Statistic.
 
                                        
                    - 
                        
                     
                    
                    
                                        
                    -