Log-Series Distribution

Random generation for the log-series distribution.

Usage

rlseries(n, size, fisher_alpha, show_progress = TRUE, check_arguments = TRUE)

Arguments

n

the number of observations.

size

The size of the distribution.

fisher_alpha

Fisher's \(\alpha\) in the log-series distribution.

show_progress

if TRUE, a progress bar is shown during long computations.

check_arguments

if TRUE, the function arguments are verified. Should be set to FALSE to save time when the arguments have been checked elsewhere.

Value

A numeric vector with the random values drawn from the log-series distribution.

Details

Fast implementation of the random generation of a log-series distribution (Fisher et al. 1943) .

The complete set of functions (including density, distribution function and quantiles) can be found in package sads but this implementation of the random generation is much faster.

If size is too large, i.e. size + 1 can't be distinguished from size due to rounding, then an error is raised.

References

Fisher RA, Corbet AS, Williams CB (1943). “The Relation between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population.” Journal of Animal Ecology, 12, 42–58. doi:10.2307/1411 .

Examples

# Generate a community made of 10000 individuals with alpha=40
size <- 1E4
fisher_alpha <- 40
species_number <- fisher_alpha * log(1 + size / fisher_alpha)
abundances <- rlseries(species_number, size = 1E5, fisher_alpha = 40)
# rcommunity() may be a better choice here
autoplot(rcommunity(1, size = 1E4, fisher_alpha = 40, distribution = "lseries"))