Editing Dirichlet distribution (section)

===When each alpha is 1/2 and relationship to the hypersphere===
When {{math|1=''α''{{sub|1}} = ... = ''α''{{sub|''K''}} = 1/2}}, a sample from the distribution can be found by randomly drawing {{mvar|K}} values independently from the standard normal distribution, squaring these values, and normalizing them by dividing by their sum, to give {{math|''x''{{sub|1}}}}, ..., {{math|''x''{{sub|''K''}}}}.

A point {{math|(''x''{{sub|1}}}}, ..., {{math|''x''{{sub|''K''}})}} can be drawn uniformly at random from the ({{math|''K''−1}})-dimensional unit hypersphere (which is the surface of a {{mvar|K}}-dimensional [[Ball (mathematics)|hyperball]]) via a similar procedure.  Randomly draw {{mvar|K}} values independently from the standard normal distribution and normalize these coordinate values by dividing each by the constant that is the square root of the sum of their squares.