58 lines
1.5 KiB
R
58 lines
1.5 KiB
R
#' @title Generates random number from a Gamma distribution
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#' @description Generates one random number from shape parameter a and rate parameter b
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#' @param a shape
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#' @param b rate
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#' @return One realization of Gamma(a, b)
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#' @details The generated random variable has mean a / b. It will be positively-skewed for small values, but converges to a symmetric distribution for very large numbers of a and b.
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randga <- function(a, b) {
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flag <- 0
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if (a > 1) {
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c1 <- a - 1
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c2 <- (a - (1 / (6 * a))) / c1
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c3 <- 2 / c1
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c4 <- c3 + 2
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c5 <- 1 / sqrt(a)
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U1 <- 1
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while (flag == 0) {
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if (a <= 2.5) {
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U1 <- rand()
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U2 <- rand()
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} else {
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while (!(U1 > 0 & U1 < 1)) {
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U1 <- rand()
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U2 <- rand()
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U1 <- U2 + c5 * (1 - 1.86 * U1)
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}
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}
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W <- c2 * U2 / U1
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if (c3 * U1 + W + (1 / W) <= c4) {
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flag <- 1
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g <- c1 * W / b
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} else if (c3 * log(U1) - log(W) + W < 1) {
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flag <- 1
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g <- c1 * W / b
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} else {
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U1 <- -1
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}
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}
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} else if (a == 1) {
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g <- sum(-(1 / b) * log(rand(a, 1)))
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} else {
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while (flag == 0) {
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U <- rand(2, 1)
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if (U[1] > exp(1) / (a + exp(1))) {
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g <- -log(((a + exp(1)) * (1 - U[1])) / (a * exp(1)))
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if (U[2] <= g^(a - 1)) {
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flag <- 1
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}
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} else {
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g <- ((a + exp(1)) * U[1] / ((exp(1))^(1 / a)))
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if (U[2] <= exp(-g)) {
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flag <- 1
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}
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}
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}
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g <- g / b
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}
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return(g)
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}
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