dgs {sads} | R Documentation |

Density, distribution function, quantile function and random generation for
the Geometric Series distribution, with parameter `k`

.

dgs( x, k, S, log = FALSE ) pgs( q, k, S, lower.tail = TRUE, log.p = FALSE ) qgs( p, k, S, lower.tail = TRUE, log.p = FALSE ) rgs( n, k, S )

`x` |
vector of (non-negative integer) quantiles. In the context of species abundance distributions, this is a vector of abundance ranks of species in a sample. |

`n` |
number of random values to return. |

`k` |
positive real, 0 < k < 1; geometric series coefficient; the ratio between the abundances of i-th and (i+1)-th species. |

`q` |
vector of (non-negative integer) quantiles. In the context of species abundance distributions, a vector of abundance ranks of species in a sample. |

`p` |
vector of probabilities. |

`S` |
positive integer 0 < S < Inf, number of elements in a collection. In the context of species abundance distributions, the number of species in a sample. |

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

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

The Geometric series distribution gives the probability (or expected proportion of occurrences) of the i-th most abundant element in a collection:

*p(i) = C * k * (1-k)^(i-1)*

where C is a normalization constant which makes the summation of p(i) over S equals to one:

*C = 1/(1 - (1-k)^S)*

where S is the number of species in the sample.

Therefore, `[dpq]gs`

can be used as rank-abundance model
for species ranks in a sample or biological community
see `fitrad-class`

.

`dgs`

gives the (log) density and `pgs`

gives the (log)
distribution function of ranks, and `qgs`

gives the
corresponding quantile function.

The Geometric series is NOT the same as geometric distribution. In
the context of community ecology, the first can be used
as a rank-abundance model and the former as a species-abundance
model. See `fitsad`

and `fitrad`

and vignettes
of sads package.

Paulo I Prado prado@ib.usp.br and Murilo Dantas Miranda.

Doi, H. and Mori, T. 2012. The discovery of species-abundance
distribution in an ecological community. *Oikos 122:* 179–182.

May, R.M. 1975. Patterns of Species Abundance and Diversity. In
Cody, M.L. and Diamond, J.M. (Eds) *Ecology and Evolution of
Communities*. Harvard University Press. pp 81–120.

`fitgs`

, `fitrad`

to fit the Geometric series as a
rank-abundance model.

x <- 1:25 PDF <- dgs(x=x, k=0.1, S=25) CDF <- pgs(q=x, k=0.1, S=25) par(mfrow=c(1,2)) plot(x,CDF, ylab="Cumulative Probability", type="b", main="Geometric series distribution, CDF") plot(x,PDF, ylab="Probability, log-scale", type="h", main="Geometric series distribution, PDF", log="y") par(mfrow=c(1,1)) ## quantile is the inverse of CDF all.equal(qgs(CDF, k=0.1, S=25), x)

[Package *sads* version 0.4.2 Index]