For n draws from a Dirichlet process with precision
alpha, returns \(E[K_n] = \sum_{i=1}^{n} \alpha /
(\alpha + i - 1)\) and \(Var[K_n] = \sum_{i=1}^{n} \alpha (i - 1) /
(\alpha + i - 1)^2\).
Usage
morie_gh_dp_ndistinct(n, alpha)
Arguments
- n
sample size (positive integer)
- alpha
Dirichlet-process precision (positive)
Value
list with elements mean and var, the expected
number of distinct values and its variance
References
Ghosal, S. and van der Vaart, A. (2017).
Fundamentals of Nonparametric Bayesian Inference.
Cambridge University Press.
Examples
morie_gh_dp_ndistinct(n = 50, alpha = 2)
#> $mean
#> [1] 7.037626
#>
#> $var
#> [1] 4.535558
#>
