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Arthur Danjou
2024-09-25 14:55:34 +02:00
parent e8c2656c1e
commit c922458740
1 changed files with 16 additions and 17 deletions
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33
M1/Monte Carlo Methods/Exercise2.rmd
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@@ -4,7 +4,7 @@
```{r}
n <- 10000
u <- runif(n)
x <- -1/2 * log(1-u)
x <- -1 / 2 * log(1 - u)
hist(x, breaks = 50, freq = FALSE)
curve(dexp(x, rate = 2), add = TRUE, col = "red")
@@ -19,9 +19,9 @@ n <- 10000
d <- 10
S <- numeric(n)
for (i in 1:n) {
u <- runif(d)
x <- -1/lambda * log(1-u)
S[i] <- sum(x)
u <- runif(d)
x <- -1 / lambda * log(1 - u)
S[i] <- sum(x)
}
hist(S, freq = FALSE, breaks = 50)
curve(dgamma(x, shape = d, rate = lambda), add = TRUE, col = "red")
@@ -29,19 +29,18 @@ curve(dgamma(x, shape = d, rate = lambda), add = TRUE, col = "red")
### Question 3
```{r}
lambda <- 4
n <- 10000
X <- numeric(n)
p <- 1
for (i in 1:n) {
S <- -1/lambda * log(1-runif(1))
while (S <= 1) {
S <- x - 1/lambda * log(1-runif(1))
p <- p+1
}
X[i] <- p
p <- 1
S <- numeric(n)
i <- 1
for (j in (1:n)) {
x <- -1 / 4 * log(1 - runif(1))
while (x <= 1) {
i <- i + 1
x <- x - 1 / 4 * log(1 - runif(1))
}
S[j] <- i
i <- 1
}
hist(X, freq = FALSE, breaks = 50)
curve(dpois(x, lambda), add = TRUE, col = "red")
hist(S, freq = FALSE)
# curve(dpois(S, lambda = 4), add = TRUE, col = "red")
```