Do we have a name for the 3-Point-Distribution?

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  • The Two-Point-Distribution is also known as the Bernoulli Distribution and is quite prominent.
  • Would imagine a Three-Point-Distribution to be fairly common as well (say probabilities of not just going up or down, but going down, staying neutral or going up); however it does not seems to be the case.
  • Is there a name for the 3-Point Distribution or more generically $n$-Point Distribution?