dgambin {gambin}

The mixture gambin distribution

Description

Density, distribution function, quantile function and random generation for the mixture gambin distribution.

Usage

dgambin(x, alpha, maxoctave, w = 1, log = FALSE)

pgambin(q, alpha, maxoctave, w = 1, lower.tail = TRUE, log.p = FALSE)

rgambin(n, alpha, maxoctave, w = 1)

qgambin(p, alpha, maxoctave, w = 1, lower.tail = TRUE, log.p = FALSE)

gambin_exp(alpha, maxoctave, w = 1, total_species)

Arguments

x

vector of (non-negative integer) quantiles.

alpha

The shape parameter of the GamBin distribution.

maxoctave

The scale parameter of the GamBin distribution - which octave is the highest in the empirical dataset?

w

A vector of weights. Default, a single weight. This vector must of the same length as alpha.

log

logical; If TRUE, probabilities p are given as log(p).

q

vector of quantiles.

lower.tail

logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].

log.p

logical; if TRUE, probabilities p are given as log(p).

n

number of random values to return.

p

vector of probabilities.

total_species

The total number of species in the empirical dataset

Details

dgambin gives the distribution function of a mixture gambin, so all octaves sum to 1. gambin_exp multiplies this by the total number of species to give the expected GamBin distribution in units of species, for comparison with empirical data.

Value

A vector with length MaxOctave + 1 of the expected number of species in each octave

References

Matthews, T. J., Borregaard, M. K., Gillespie, C. S., Rigal, F., Ugland, K. I., Krüger, R. F., . . . Whittaker, R. J. (2019) Extension of the gambin model to multimodal species abundance distributions. Methods in Ecology and Evolution, doi:10.1111/2041-210X.13122

Matthews, T.J., Borregaard, M.K., Ugland, K.I., Borges, P.A.V, Rigal, F., Cardoso, P. and Whittaker, R.J. (2014) The gambin model provides a superior fit to species abundance distributions with a single free parameter: evidence, implementation and interpretation. Ecography 37: 1002-1011.

Examples

## maxoctave is 4. So zero for x = 5
dgambin(0:5, 1, 4)

## Equal weightings between components
dgambin(0:5, alpha = c(1,2), maxoctave = c(4, 4))

## Zero weight on the second component, i.e. a 1 component model
dgambin(0:5, alpha = c(1,2), maxoctave = c(4, 4), w = c(1, 0))
expected = gambin_exp(4, 13, total_species = 200)
plot(expected, type = "l")

##draw random values from a gambin distribution 
x = rgambin(1e6, alpha = 2, maxoctave = 7) 
x = table(x)
freq = as.vector(x)
values = as.numeric(as.character(names(x)))
abundances = data.frame(octave=values, species = freq)
fit_abundances(abundances, no_of_components = 1)