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--- people:kargin:math447:r_examples [2016/03/05 15:31]
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+++ people:kargin:math447:r_examples [2016/03/05 15:40] (current)
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+== Examples of R-code ==
+=== Example: Approximation of the Gaussian distribution by sums of Bernoulli and uniform random variables. ===
+<code>
+#Generating data
+repet <- 10000
+size <- 100
+p <- .5
+data <- (rbinom(repet, size, p) - size * p) / sqrt(size * p * (1-p))
+hist(data, freq = FALSE)
+#Histograms
+#By default you get a frequency histogram.
+#To get a density you set "freq = FALSE".
+#To control the number of bins use "breaks = ".
+hist(data, breaks = size/2, col = 'red', freq = FALSE)
+#Plotting the pdf of the normal distribution
+x <- seq(min(data) - 1, max(data) + 1, .01)
+lines(x, dnorm(x), col='green', lwd = 4)
+#similar exercise for uniform random variables.
+size <- 3
+data <- runif(repet * size)
+data.matrix  <- matrix(data, nrow = size)
+mu <- size * 1/2
+sigma <- sqrt(size * 1/12)
+data <- (colSums(data.matrix) - mu )/ sigma
+hist(data, breaks = 100, col = 'red', freq = FALSE)
+lines(x, dnorm(x), col = 'green', lwd = 4)
+</code>