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66 lines
1.2 KiB
Plaintext
66 lines
1.2 KiB
Plaintext
# Exercise 8 - a : Truncated Normal Distribution
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```{r}
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f <- function(x, b, mean, sd) {
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1 / (sqrt(2 * pi * sd^2) * pnorm((mean - b) / sd)) *
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exp(-(x - mean)^2 / (2 * sd^2)) *
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(x >= b)
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}
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M <- function(b, mean, sd) {
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1 / pnorm((mean - b) / sd)
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}
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g <- function(x, b, mean, sd) {
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1 / sqrt(2 * pi * sd^2) *
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exp(-(x - mean)^2 / (2 * sd^2))
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}
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n <- 10000
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mean <- 0
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sd <- 2
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b <- 2
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x <- numeric(0)
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while (length(x) < n) {
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U <- runif(1)
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X <- rnorm(1, mean, sd)
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x <- append(x, X[U <= (f(X, b, mean, sd) / (M(b, mean, sd) * g(X, b, mean, sd)))])
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}
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t <- seq(b, 7, 0.01)
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hist(x, freq = FALSE, breaks = 35)
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lines(t, f(t, b, mean, sd), col = "red", lwd = 2)
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```
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# Exercise 8 - b : Truncated Exponential Distribution
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```{r}
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f <- function(x, b, lambda) {
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lambda * exp(-lambda * (x - b)) * (x >= b)
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}
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M <- function(b, lambda) {
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exp(lambda * b)
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}
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g <- function(x, lambda) {
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lambda * exp(-lambda * x)
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}
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n <- 10000
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b <- 2
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lambda <- 1
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x <- numeric(0)
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while (length(x) < n) {
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U <- runif(1)
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X <- rexp(1, lambda)
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x <- append(x, X[U <= (f(X, b, lambda) / (M(b, lambda) * g(X, lambda)))])
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}
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t <- seq(b, 7, 0.01)
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hist(x, freq = FALSE, breaks = 35)
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lines(t, f(t, b, lambda), col = "red", lwd = 2)
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```
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