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**Package: **prob**Superclasses: **prob.ParametricTruncatableDistribution

Multinomial probability distribution object

`prob.MultinomialDistribution`

is an object
consisting of parameters and a model description for a multinomial
probability distribution. Create a probability distribution object
with specified parameters using `makedist`

.

creates
a multinomial probability distribution object using the default parameter
values.`pd`

= makedist('Multinomial')

creates
a multinomial distribution object using the specified parameter value.`pd`

= makedist('Multinomial','Probabilities',`probabilities`

)

cdf | Cumulative distribution function of probability distribution object |

icdf | Inverse cumulative distribution function of probability distribution object |

iqr | Interquartile range of probability distribution object |

median | Median of probability distribution object |

Probability density function of probability distribution object | |

random | Generate random numbers from probability distribution object |

truncate | Truncate probability distribution object |

mean | Mean of probability distribution object |

std | Standard deviation of probability distribution object |

var | Variance of probability distribution object |

The multinomial distribution is a generalization of the binomial
distribution. While the binomial distribution gives the probability
of the number of "successes" in *n* independent
trials of a two-outcome process, the multinomial distribution gives
the probability of each combination of outcomes in *n* independent
trials of a *k*-outcome process. The probability
of each outcome in any one trial is given by the fixed probabilities *p*_{1},
..., *p*_{k}.

The multinomial distribution uses the following parameters.

Parameter | Description | Support |
---|---|---|

`probabilities` | Outcome probabilities | $$0\le probabilities\left(i\right)\le 1\text{\hspace{0.17em}};\text{\hspace{0.17em}}{\displaystyle \sum _{all\left(i\right)}probabilities\left(i\right)}=1$$ |

The probability density function (pdf) is

$$f\left(x|n,p\right)=\frac{n!}{{x}_{1}!\dots {x}_{k}!}{p}_{1}{}^{{x}_{1}}\cdots {p}_{k}{}^{{x}_{k}}\text{\hspace{1em}};\text{\hspace{1em}}{\displaystyle \sum _{1}^{k}{x}_{i}=n}\text{\hspace{0.17em}},\text{\hspace{0.17em}}{\displaystyle \sum _{1}^{k}{p}_{i}=1}\text{\hspace{0.17em}},$$

where *x* = (*x*_{1},...,*x _{k}*)
gives the number of each

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