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47 lines
811 B
Plaintext
47 lines
811 B
Plaintext
# Exercise 2 : Exponential distribution and related distributions
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### Question 1
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```{r}
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n <- 10000
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u <- runif(n)
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x <- -1 / 2 * log(1 - u)
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hist(x, breaks = 50, freq = FALSE)
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curve(dexp(x, rate = 2), add = TRUE, col = "red")
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qqplot(x, rexp(n, rate = 2))
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```
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### Question 2
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```{r}
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lambda <- 1.5
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n <- 10000
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d <- 10
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S <- numeric(n)
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for (i in 1:n) {
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u <- runif(d)
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x <- -1 / lambda * log(1 - u)
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S[i] <- sum(x)
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}
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hist(S, freq = FALSE, breaks = 50)
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curve(dgamma(x, shape = d, rate = lambda), add = TRUE, col = "red")
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```
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### Question 3
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```{r}
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n <- 10000
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S <- numeric(n)
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i <- 1
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for (j in (1:n)) {
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x <- -1 / 4 * log(1 - runif(1))
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while (x <= 1) {
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i <- i + 1
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x <- x - 1 / 4 * log(1 - runif(1))
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}
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S[j] <- i
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i <- 1
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}
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hist(S, freq = FALSE)
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curve(dpois(S, lambda = 4), add = TRUE, col = "red")
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```
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