| Title: | Ewens Distribution |
| Version: | 0.1.0 |
| Description: | Implements the probability mass function of, and random draws from, the Ewens distribution, a probability distribution over partitions of integer, as described in Ewens (1972) <doi:10.1016/0040-5809(72)90035-4>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| URL: | https://github.com/chrishanretty/ewens |
| BugReports: | https://github.com/chrishanretty/ewens/issues |
| RoxygenNote: | 7.3.2 |
| Imports: | copula (≥ 1.0) |
| Suggests: | knitr, quarto |
| VignetteBuilder: | quarto |
| NeedsCompilation: | yes |
| Packaged: | 2026-05-14 11:01:47 UTC; chanret |
| Author: | Chris Hanretty 
[aut, cre] |
| Maintainer: | Chris Hanretty <chris.hanretty@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2026-05-19 09:30:14 UTC |
Probability mass function for the Ewens distribution
Description
Gives the probability mass function for the Ewens distribution, as described in Ewens, Warren (1972). "The sampling theory of selectively neutral alleles". Theoretical Population Biology. 3: 87–112. doi:10.1016/0040-5809(72)90035-4.
Usage
dewens(x, theta = 1, log = FALSE)
Arguments
x |
A vector giving class memberships of each observation in the sample |
theta |
A non-negative parameter governing the expected sample diversity. |
log |
if TRUE, probabilities are given as log(p). Default is FALSE. |
Details
The probability of a vector of counts m_1, ..., m_n is given by the expression
\frac{n!}{\theta (\theta + 1) ... (\theta + n - 1)}\prod_{j=1}^n \frac{\theta^{m_j}}{j^{m_j} m_j!}
Value
A numeric vector giving a probability (or if log = TRUE, a log probability)
Examples
x <- sample(LETTERS, 120, replace = TRUE)
dewens(x, theta = 1)
dewens(x, theta = 0) ## returns NaN since vector incompatible with zero diversity
Probability mass function for the number of classes from a Ewens distribution
Description
Probability mass function for the number of classes from a Ewens distribution
Usage
dewens_k(k, n, theta)
Arguments
k |
An integer number of classes at which to evaluate the PMF |
n |
A sample size not less than k |
theta |
A non-negative parameter governing the expected sample diversity. |
Details
The number of classes from a Ewens distribution with parameter \theta is given by the expression
Pr(K = k) = \lvert{} S^k_n \rvert{} \frac{\theta^k}{\theta (\theta + 1) ... (\theta + n - 1)}
, where \lvert{}S^k_n \rvert{} is the absolute value of a Stirling number of the first kind.
Value
The probability of observing k classes
Examples
x <- sample(LETTERS, 120, replace = TRUE)
dewens_k(1, 20, theta = 1) ## Pretty unlikely we just see one class
Calculate expected number of classes in a sample of size n given theta
Description
The expected number of classes from the Ewens distribution is given by \theta \sum_{j=1}^{n} \frac{1}{\theta + j - 1}. This is often more convenient than integrating across the PMF given by dewens_k
Usage
ewens_k_exact(n, theta)
Arguments
n |
The sample size |
theta |
The non-negative parameter governing expected sample diversity |
Maximum likelihood estimate of theta given sample vector with class memberships
Description
Maximum likelihood estimate of theta given sample vector with class memberships
Usage
ewens_mle(x)
Arguments
x |
A vector containing class memberships; sample size n and number of classes k are calculated from this |
Value
A scalar giving the estimate of theta
Draw from a generalized Chinese Restaurant Process
Description
Draw from a generalized Chinese Restaurant Process
Usage
gcrp(n, alpha = 0, theta = 1)
Arguments
n |
The sample size. |
alpha |
A parameter between zero and one inclusive governing the expected sample diversity |
theta |
A non-negative parameter governing the expected sample diversity. |
Value
A vector of length n consisting of numeric class labels.
Examples
rewens(100, 1)
rewens(120, 0.5)
rewens(10, 0)
Draw from the Ewens distribution
Description
Returns a vector with class membership
Usage
rewens(n, theta = 1)
Arguments
n |
The sample size. |
theta |
A non-negative parameter governing the expected sample diversity. |
Details
Although this command is described as sampling from the Ewens distribution, it is easier to think of it as a particular instantiation of the Chinese Restaurant Process, run for n "customers". The $j$th customer
sits at a new table with probability
\frac{\theta}{j - 1 + \theta}, orsits at an occupied table with probability
\frac{c}{j - 1 + \theta}where $c$ is the number of customers already at each table.
Value
A vector of length n consisting of numeric class labels.
Examples
rewens(100, 1)
rewens(120, 0.5)
rewens(10, 0) ## equal to rep(1, 10)
Draw from the Griffiths-Engen-McCloskey distribution
Description
Draw from the Griffiths-Engen-McCloskey distribution
Usage
rgem(alpha = 0, theta = 1, trunc_at = 500)
Arguments
alpha |
A parameter between zero and one |
theta |
A parameter which must be greater than -alpha |
trunc_at |
An integer which specifies the maximum number of components to return |
Details
The Griffiths-Engen-McCloskey distribution is the infinite dimensional counterpart to the Ewens sampling distribution. This function does not return an infinite dimensional vector(!), but returns a vector of shares creating by a "stick-breaking" construction. The vector of shares is returned after trunc_at sticks are broken; this can mean that there is still a non-negligible residual amount.
Value
A vector of shares of length trunc_at which may sum to less than one