Adiciona script de distribuição amostral.

scripts/02_R_distr.R

+#=======================================================================
+# Distribuição amostral da amplitude.
+
+n <- 5     # Tamanho da amostra.
+sigma <- 1 # Desvio-padrão populacional
+
+w <- replicate(1000, {
+    x <- rnorm(n = n, m = 0, sd = sigma)
+    r <- diff(range(x))/sigma
+    r/sigma
+}
+               )
+
+plot(density(w))
+rug(w)
+
+plot(ecdf(w))
+rug(w)
+
+mean(w)
+sd(w)
+
+curve(pnorm(x, mean = mean(w), sd = sd(w)), add = TRUE, col = 2)
+
+#-----------------------------------------------------------------------
+# Fazer para diferentes valores de n.
+
+nvals <- c(2, 3, 4, 5, 7, 10, 15)
+
+ww <- lapply(nvals,
+             function(n) {
+                 replicate(1000, {
+                     x <- rnorm(n = n, m = 0, sd = sigma)
+                     r <- diff(range(x))/sigma
+                     r/sigma
+                 })
+             })
+str(ww)
+
+t(sapply(ww, length))
+
+da <- data.frame(n = ordered(rep(nvals, sapply(ww, length))),
+                 w = do.call(c, ww))
+
+aggregate(w ~ n, data = da, FUN = function(x) c(mean(x), sd(x)))
+
+library(latticeExtra)
+
+densityplot(~w | n, data = da, n = 202, as.table = TRUE,
+            auto.key = list(corner = c(0.9, 0.1)),
+            panel = function(x, ...) {
+                panel.densityplot(x = x, ...)
+                panel.mathdensity(dmath = dnorm, col = "black",
+                                  args = list(mean = mean(x),
+                                              sd = sd(x)))
+            })
+
+ecdfplot(~w | n, data = da, as.table = TRUE,
+         auto.key = list(corner = c(0.9, 0.1)),
+         panel = function(x, subscripts, ...) {
+             panel.ecdfplot(x, subscripts = subscripts, ...)
+             m <- mean(x)
+             s <- sd(x)
+             col <- "gray50"
+             panel.curve(pnorm(x, mean = m, sd = s), col = col)
+             panel.abline(v = m, lty = 2, col = col)
+         })
+
+ecdfplot(~w, groups = n, data = da,
+         auto.key = list(corner = c(0.9, 0.1)))