I am trying to understand exactly what information the graph of a multinomial distribution is supposed to convey.
The thing I find strange is that a binomial distribution is graphed in two dimensions and contains information about two fundamental outcomes, i.e., heads and tails on a coin. I would expect the three dimensional graph of a multinomial distribution to describe a "three sided coin," but Mathematica only allows input of two outcomes, which must also sum to probability [imath]1[/imath]. The multinomial distribution graph in three dimensions seems to contain exactly the same information as the binomial distribution in two dimensions. In fact, the nonzero data can be seen (in the above example and in the documentation) to be contained within a two-dimensional diagonal slice of three-dimensional space.
Should a three-dimensional multinomial distribution PMF describe three fundamental outcomes, or if not, what does the extra dimension achieve?
The thing I find strange is that a binomial distribution is graphed in two dimensions and contains information about two fundamental outcomes, i.e., heads and tails on a coin. I would expect the three dimensional graph of a multinomial distribution to describe a "three sided coin," but Mathematica only allows input of two outcomes, which must also sum to probability [imath]1[/imath]. The multinomial distribution graph in three dimensions seems to contain exactly the same information as the binomial distribution in two dimensions. In fact, the nonzero data can be seen (in the above example and in the documentation) to be contained within a two-dimensional diagonal slice of three-dimensional space.
Should a three-dimensional multinomial distribution PMF describe three fundamental outcomes, or if not, what does the extra dimension achieve?