R/dispfit-package.R

In apferreira/dispfit: Fit distributions to species dispersal data

#' dispfit: A package to estimate species dispersal kernels
#'
#' The dispfit package fits several pre-defined distributions to dispersal or movement data,
#' computing several estimators: AIC, AICc, BIC, Chi-squared, and Kolgomorov-Smirnov.
#' It also estimates the parameter(s) value(s) and CI of each distribution,
#' as well as its Mean, Variance, Skewness, and Kurtosis.
#'
#'@details
#' The dispfit package fits 9 well-known distributions for estimating dispersal kernels
#' (Clark et al., 1999; Nathan et al., 2012).
#' The simplest functions considered are the single‐parameter Rayleigh and Exponential,
#' which are particularly popular in mathematical developments of theory concerning spatial dynamics
#' (O'Dwyer & Green 2010; Gilbert et al. 2014; Harsch et al. 2014).
#' The remaining 7 functions are two-parameter distributions which are often referred to better
#' represent real dispersal kernels than Rayleigh and Exponential functions
#' (Bullock and Clarke, 2000; Clark et al., 1999).
#'
#' @section Package functions:
#' dispfit includes two main functions:
#' \tabular{ll}{
#'   \code{\link{dispersal.kernel}} \tab Fits several pre-defined distributions to dispersal or movement data. \cr
#'   \code{\link{plot.dispfit}} \tab Plots the distributions previously fitted by dispersal.kernel. \cr
#' }
#'
#' @section Probability density function:
#' Assuming that a single point is the origin site of all dispersers,
#' then the dispersal distance of each disperser is the Euclidian distance between the origin and its end point.
#' The dispersal distances of all dispersers reflect a continuous parametric distribution,
#' or probability density function (pdf), that characterizes the studied population.
#' A dispersal kernel is then defined as the pdf of the distribution of the values
#' of the Euclidean distances between the source and the final location of a dispersal event.
#' There are several characterizations of a dispersal kernel,
#' for instance Nathan et al. (2012) distinguish between “dispersal distance kernel, KD”,
#' and “dispersal location kernel, KL”.
#'
#' @section Distributions:
#'
#' \describe{
#' \item{Rayleigh}{\deqn{f(r) = 1/(\pi a^2) * exp(-(r/a)^2)}}
#' \item{Exponential}{\deqn{f(r) = 1/(2\pi a^2) * exp(-r/a)}}
#' \item{Generalized Normal}{\deqn{f(r) = b/(2\pi (a^2) \Gamma(2/b)) * exp(-(r/a) ^ b)}}
#' \item{Bivariate Student’s t (2\emph{Dt)}}{\deqn{f(r) =  (b-1) / (\pi (a^2)) * [1 + (r/a)^2) ^ -b]}}
#' \item{Geometric}{\deqn{f(r) = (b - 2)(b - 1) / 2\pi (a^2) * (1 + r/a) ^ -b}}
#' \item{Lognormal}{\deqn{f(r) = 1 / ((2\pi) ^ (3/2) b (r ^ 2)) * exp(- log(r / a)^2 / (2 b^2))}}
#' \item{Wald}{\deqn{f(r) = \sqrt(b)/\sqrt(8 \pi^3 r^5) * exp(-(b (r - a)^2)/2 (a^2) r)}}
#' \item{Weibull}{\deqn{f(r) = b/2\pi a^b * r^(b-2) * exp(-(r/a)^b)}}
#' \item{Gamma}{\deqn{f(r) = 1 / 2\pi a^2 \Gamma(b) * (r/a)^(b-2) * exp(-r/a)}}
#' }
#'
#' @authors António Proença-Ferreira, \email{antoniomiguelpferreira@@gmail.com}
#' Luís Borda-de-Água
#' Miguel Porto
#' António Mira
#' Francisco Moreira
#' Ricardo Pita
#' @docType package
#'
"_PACKAGE"
#> [1] "_PACKAGE"