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Logit-normal distribution in alm(), proposed in #13
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| #' Logit Normal Distribution | ||
| #' | ||
| #' Density, cumulative distribution, quantile functions and random number | ||
| #' generation for the distribution that becomes normal after the Logit | ||
| #' transformation. | ||
| #' | ||
| #' The distribution has the following density function: | ||
| #' | ||
| #' f(y) = 1/(sqrt(2 pi) y (1-y)) exp(-(logit(y) -mu)^2 / (2 sigma^2)) | ||
| #' | ||
| #' where y is in (0, 1) and logit(y) =log(y/(1-y)). | ||
| #' | ||
| #' Both \code{plogitnorm} and \code{qlogitnorm} are returned for the lower | ||
| #' tail of the distribution. | ||
| #' | ||
| #' All the functions are defined for the values between 0 and 1. | ||
| #' | ||
| #' @template author | ||
| #' @keywords distribution | ||
| #' | ||
| #' @param q vector of quantiles. | ||
| #' @param p vector of probabilities. | ||
| #' @param n number of observations. Should be a single number. | ||
| #' @param mu vector of location parameters (means). | ||
| #' @param sigma vector of scale parameters. | ||
| #' @param log if \code{TRUE}, then probabilities are returned in | ||
| #' logarithms. | ||
| #' | ||
| #' @return Depending on the function, various things are returned | ||
| #' (usually either vector or scalar): | ||
| #' \itemize{ | ||
| #' \item \code{dlogitnorm} returns the density function value for the | ||
| #' provided parameters. | ||
| #' \item \code{plogitnorm} returns the value of the cumulative function | ||
| #' for the provided parameters. | ||
| #' \item \code{qlogitnorm} returns quantiles of the distribution. Depending | ||
| #' on what was provided in \code{p}, \code{mu} and \code{sigma}, this | ||
| #' can be either a vector or a matrix, or an array. | ||
| #' \item \code{rlogitnorm} returns a vector of random variables | ||
| #' generated from the logitnorm distribution. Depending on what was | ||
| #' provided in \code{mu} and \code{sigma}, this can be either a vector | ||
| #' or a matrix or an array. | ||
| #' } | ||
| #' | ||
| #' @examples | ||
| #' x <- dlogitnorm(c(-1000:1000)/200, 0, 1) | ||
| #' plot(c(-1000:1000)/200, x, type="l") | ||
| #' | ||
| #' x <- plogitnorm(c(-1000:1000)/200, 0, 1) | ||
| #' plot(c(-1000:1000)/200, x, type="l") | ||
| #' | ||
| #' qlogitnorm(c(0.025,0.975), 0, c(1,2)) | ||
| #' | ||
| #' x <- rlogitnorm(1000, 0, 1) | ||
| #' hist(x) | ||
| #' | ||
| #' @references \itemize{ | ||
| #' \item Mead, R. (1965). A Generalised Logit-Normal Distribution. | ||
| #' Biometrics, 21 (3), 721–732. doi: 10.2307/2528553 | ||
| #' } | ||
| #' | ||
| #' @rdname logitnorm-distribution | ||
| #' @importFrom stats dnorm pnorm qnorm rnorm | ||
| #' @export dlogitnorm | ||
| dlogitnorm <- function(q, mu=0, sigma=1, log=FALSE){ | ||
| logitnormReturn <- 1 / (sigma*sqrt(2*pi)*q*(1-q))*exp(-(log(q/(1-q))-mu)^2/(2*sigma^2)); | ||
| # logitnormReturn[q<=0] <- -Inf; | ||
| # logitnormReturn[q>=1] <- Inf; | ||
|
|
||
| # Return logs if needed | ||
| if(log){ | ||
| logitnormReturn[] <- log(logitnormReturn); | ||
| } | ||
|
|
||
| return(logitnormReturn); | ||
| } | ||
|
|
||
| #' @rdname logitnorm-distribution | ||
| #' @export plogitnorm | ||
| #' @aliases plogitnorm | ||
| plogitnorm <- function(q, mu=0, sigma=1){ | ||
| logitnormReturn <- vector("numeric", length(q)); | ||
| logitnormReturn[q>=0] <- pnorm(q=log(q/(1-q)), mean=mu, sd=sigma); | ||
| logitnormReturn[q<0] <- 0; | ||
| logitnormReturn[q>=1] <- 1; | ||
| return(logitnormReturn); | ||
| } | ||
|
|
||
| #' @rdname logitnorm-distribution | ||
| #' @export qlogitnorm | ||
| #' @aliases qlogitnorm | ||
| qlogitnorm <- function(p, mu=0, sigma=1){ | ||
| logitnormReturn <- qnorm(p=p, mean=mu, sd=sigma); | ||
| logitnormReturn[] <- exp(logitnormReturn)/(1+exp(logitnormReturn)); | ||
| logitnormReturn[is.nan(logitnormReturn)] <- 0; | ||
| return(logitnormReturn); | ||
| } | ||
|
|
||
| #' @rdname logitnorm-distribution | ||
| #' @export rlogitnorm | ||
| #' @aliases rlogitnorm | ||
| rlogitnorm <- function(n=1, mu=0, sigma=1){ | ||
| logitnormReturn <- qlogitnorm(runif(n=n, 0, 1), mu=mu, sigma=sigma); | ||
| return(logitnormReturn); | ||
| } |
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