NegativeMultinomialDistribution
NegativeMultinomialDistribution[n,p]
represents a negative multinomial distribution with parameter n and failure probability vector p.
更多信息和选项
- To use NegativeMultinomialDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].
- The probability for a vector x of non-negative integers x1, x2, …, xLength[p] in a negative multinomial distribution is proportional to (n-1+∑xi)!∏(pixi/xi!).
- The parameter n can be any positive real number, and p can be any vector of non-negative real numbers that sum to less than unity.
- If n is a positive integer, NegativeMultinomialDistribution[n,p] gives the distribution of the failure counts in a sequence of trials with success probability 1-Total[p] and Length[p] types of failure before n successes occur.
- NegativeMultinomialDistribution can be used with such functions as Mean, CDF, and RandomInteger.
范例
打开所有单元 关闭所有单元基本范例 (3)
Needs["MultivariateStatistics`"]The mean of a negative multinomial distribution:
Mean[NegativeMultinomialDistribution[n, {Subscript[p, 1], Subscript[p, 2], Subscript[p, 3]}]]Needs["MultivariateStatistics`"]The variances of each dimension:
Variance[NegativeMultinomialDistribution[n, {Subscript[p, 1], Subscript[p, 2], Subscript[p, 3]}]]Needs["MultivariateStatistics`"]PDF[NegativeMultinomialDistribution[n, {Subscript[p, 1], Subscript[p, 2], Subscript[p, 3]}], {x, y, z}]Scope (3)
Needs["MultivariateStatistics`"]Generate a set of pseudorandom vectors that follow a negative multinomial distribution:
RandomInteger[NegativeMultinomialDistribution[20, {.2, .3, .1}], 10]Needs["MultivariateStatistics`"]Skewness[NegativeMultinomialDistribution[n, {Subscript[p, 1], Subscript[p, 2], Subscript[p, 3]}]]Needs["MultivariateStatistics`"]Kurtosis[NegativeMultinomialDistribution[n, {Subscript[p, 1], Subscript[p, 2], Subscript[p, 3]}]]Properties & Relations (1)
Needs["MultivariateStatistics`"]A univariate negative multinomial distribution is a negative binomial distribution:
PDF[NegativeMultinomialDistribution[n, {1 - p}], {x}]PDF[NegativeBinomialDistribution[n, p], x]FullSimplify[% == %%]Possible Issues (2)
Needs["MultivariateStatistics`"]NegativeMultinomialDistribution is not defined when n is not a positive integer:
Mean[NegativeMultinomialDistribution[-2, {Subscript[p, 1], Subscript[p, 2], Subscript[p, 3], Subscript[p, 4]}]]
NegativeMultinomialDistribution is not defined when p is not a vector of probabilities that sums to less than 1:
Mean[NegativeMultinomialDistribution[n, {1 / 2, 2}]]
Needs["MultivariateStatistics`"]Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
Mean[NegativeMultinomialDistribution[n, {Subscript[p, 1], Subscript[p, 2], Subscript[p, 3]}]] /. {n -> -5, Subscript[p, 1] -> 1 / 2, Subscript[p, 2] -> 2, Subscript[p, 3] -> I}文本
Wolfram Research (2007)，NegativeMultinomialDistribution，Wolfram 语言函数，https://reference.wolfram.com/language/MultivariateStatistics/ref/NegativeMultinomialDistribution.html.
CMS
Wolfram 语言. 2007. "NegativeMultinomialDistribution." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/MultivariateStatistics/ref/NegativeMultinomialDistribution.html.
APA
Wolfram 语言. (2007). NegativeMultinomialDistribution. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/MultivariateStatistics/ref/NegativeMultinomialDistribution.html 年