Chinese restaurant table distribution

Short description: probability distribution modeling number of tables in Chinese restaurant process

Chinese restaurant tableParameters|

θ>0

m∈{0,1,2,…}

|

Support|  L∈{0,1,2,…,m}
pmf|  Γ(θ)Γ(m+θ)|s(m,ℓ)|θℓ
Mean|  θ(ψ(θ+m)−ψ(θ))
(see digamma function)

In probability theory and statistics, the Chinese restaurant table distribution (CRT) is the distribution on the number of tables in the Chinese restaurant process.[1] It can be understood as the sum of n independent random variables, each with a different Bernoulli distribution:

L=∑n=1mbnbn∼Bernoulli⁡(θn−1+θ)

The probability mass function of L is given by [2]

f(ℓ)=Γ(θ)Γ(m+θ)|s(m,ℓ)|θℓ

where s denotes Stirling numbers of the first kind.

## See also

* Ewens sampling formula

## References

1. ↑ "Negative Binomial Process Count and Mixture Modeling". https://arxiv.org/abs/1209.3442.
2. ↑ Antoniak, Charles E (1974). "Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems". The Annals of Statistics.

0.00

(0 votes)

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Chinese_restaurant_table_distribution&oldid=237931"