#' @title Poisson log-normal
#'
#' @description \code{dplnorm} gives the probability mass function, \code{pplnorm} gives the cumulative mass
#' function, \code{qplnorm} the quantile function, \code{rplnorm} randome number generation
#'
#' @details These functions assume infinite support of the Poisson log-normal from [1, Inf). Calculations are based on code from the \code{poilog} package, see References
#'
#' @param x vector of integers for which to return the probability
#' @param q vector of integers for which to return the cumulative probability
#' @param p vector of probabilities for which to return the quantile
#' @param n number of random replicates
#' @param mu mean log abundance
#' @param sig standard deviation of log abundance
#' @param log logical, should the log probability be used
#' @param lower.tail logical, should the lower tail be used
#'
#' @keywords Poisson log normal, species abundance, SAD
#' @export
#'
#' @examples
#' dplnorm(1:10, 0.5, 0.1)
#'
#' @return A numeric vector of length equal to the input
#'
#' @author Andy Rominger <ajrominger@@gmail.com>
#' @seealso dpois, dlnorm, dtpois
#' @references Engen, S., R. Lande, T. Walla & P. J. DeVries. 2002. Analyzing spatial structure of communities using the two-dimensional Poisson lognormal species abundance model. American Naturalist 160: 60-73.
#' @rdname PoisLogNormal
dplnorm <- function(x, mu, sig, log=FALSE) {
out <- numeric(length(x))
out[x %% 1 == 0 & x >= 1] <- poilog::dpoilog(x[x %% 1 == 0 & x >= 1], mu, sig) / (1 - poilog::dpoilog(0, mu, sig))
if(any(x %% 1 != 0)) {
for(bad in x[x %% 1 != 0]) {
warning(sprintf('non-integer x = %s', bad))
}
}
if(log) out <- log(out)
return(out)
}
#' @export
#' @rdname PoisLogNormal
pplnorm <- function(q, mu, sig, lower.tail=TRUE, log=FALSE) {
out <- numeric(length(q))
newq <- floor(q)
newq[newq < 1] <- 1
if(length(q) > 1) {
temp <- cumsum(poilog::dpoilog(1:max(newq), mu, sig)) / (1 - poilog::dpoilog(0, mu, sig))
out <- temp[newq]
} else {
out <- sum(poilog::dpoilog(1:newq, mu, sig)) / (1 - poilog::dpoilog(0, mu, sig))
}
out[q < 1] <- 0
# if(any(q %% 1 != 0)) {
# for(bad in q[q %% 1 != 0]) {
# warning(sprintf('non-integer q = %s', bad))
# }
# }
if(!lower.tail) out <- 1 - out
if(log) out <- log(out)
return(out)
}
#' @export
#' @rdname PoisLogNormal
qplnorm <- function(p, mu, sig, lower.tail=TRUE, log=FALSE) {
if(log) p <- exp(p)
if(!lower.tail) p <- 1 - p
out <- .plnormcdfinv(p, mu, sig)
if(any(is.nan(out))) {
warning('NaNs produced')
}
return(out)
}
#' @export
#' @rdname PoisLogNormal
rplnorm <- function(n, mu, sig) {
N <- 100 * n / (1 - dpois(0, exp(mu + sig^2/2)))
lat <- rlnorm(N, mu, sig)
rel <- rpois(N, lat)
rel <- rel[rel > 0]
if(length(rel) < n) warning(sprintf('could not find %s unique random variates, using bootstrapping', n))
return(sample(rel, n, rep=ifelse(n < length(rel), FALSE, TRUE)))
}
## =================================
## helper functions
## =================================
## inverse cdf of the poisson log normal
#' @export
.plnormcdfinv <- function(p, mu, sig) {
this.cdf <- c(0, cumsum(poilog::dpoilog(1:10000, mu, sig)) / (1 - poilog::dpoilog(0, mu, sig)))
approx(x=this.cdf, y=0:10000,
xout=p, method='constant', yleft=NaN, yright=Inf, f=1)$y
}
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