# Random number generator for a truncated normal distribution Generates a random number from a truncated normal distribution. ```r rtnorm(n, mean = 0, sd = 1, lower = -Inf, upper = Inf) ``` ## Details For internal use ## Note Taken from `msm` R-package. ## Examples ```r ## The function is currently defined as function(n, mean = 0, sd = 1, lower = -Inf, upper = Inf) { if (length(n) > 1) { n <- length(n) } mean <- rep(mean, length = n) sd <- rep(sd, length = n) lower <- rep(lower, length = n) upper <- rep(upper, length = n) lower <- (lower - mean) / sd upper <- (upper - mean) / sd ind <- seq(length = n) ret <- numeric(n) alg <- ifelse(lower > upper, -1, ifelse(((lower < 0 & upper == Inf) | (lower == -Inf & upper > 0) | (is.finite(lower) & is.finite(upper) & (lower < 0) & (upper > 0) & (upper - lower > sqrt(2 * pi)))), 0, ifelse((lower >= 0 & (upper > lower + 2 * sqrt(exp(1)) / (lower + sqrt(lower^2 + 4)) * exp((lower * 2 - lower * sqrt(lower^2 + 4)) / 4))), 1, ifelse(upper <= 0 & (-lower > -upper + 2 * sqrt(exp(1)) / (-upper + sqrt(upper^2 + 4)) * exp((upper * 2 - -upper * sqrt(upper^2 + 4)) / 4)), 2, 3) ))) ind.nan <- ind[alg == -1] ind.no <- ind[alg == 0] ind.expl <- ind[alg == 1] ind.expu <- ind[alg == 2] ind.u <- ind[alg == 3] ret[ind.nan] <- NaN while (length(ind.no) > 0) { y <- rnorm(length(ind.no)) done <- which(y >= lower[ind.no] & y <= upper[ind.no]) ret[ind.no[done]] <- y[done] ind.no <- setdiff(ind.no, ind.no[done]) } stopifnot(length(ind.no) == 0) while (length(ind.expl) > 0) { a <- (lower[ind.expl] + sqrt(lower[ind.expl]^2 + 4)) / 2 z <- rexp(length(ind.expl), a) + lower[ind.expl] u <- runif(length(ind.expl)) done <- which((u <= exp(-(z - a)^2 / 2)) & (z <= upper[ind.expl])) ret[ind.expl[done]] <- z[done] ind.expl <- setdiff(ind.expl, ind.expl[done]) } stopifnot(length(ind.expl) == 0) while (length(ind.expu) > 0) { a <- (-upper[ind.expu] + sqrt(upper[ind.expu]^2 + 4)) / 2 z <- rexp(length(ind.expu), a) - upper[ind.expu] u <- runif(length(ind.expu)) done <- which((u <= exp(-(z - a)^2 / 2)) & (z <= -lower[ind.expu])) ret[ind.expu[done]] <- -z[done] ind.expu <- setdiff(ind.expu, ind.expu[done]) } stopifnot(length(ind.expu) == 0) while (length(ind.u) > 0) { z <- runif(length(ind.u), lower[ind.u], upper[ind.u]) rho <- ifelse(lower[ind.u] > 0, exp((lower[ind.u]^2 - z^2) / 2), ifelse(upper[ind.u] < 0, exp((upper[ind.u]^2 - z^2) / 2), exp(-z^2 / 2))) u <- runif(length(ind.u)) done <- which(u <= rho) ret[ind.u[done]] <- z[done] ind.u <- setdiff(ind.u, ind.u[done]) } stopifnot(length(ind.u) == 0) ret * sd + mean } ``` ## Author(s) C. H. Jackson

rtnorm function