From 24982eec99035fb2259ec1b3b5f2a1c55f774173 Mon Sep 17 00:00:00 2001
From: Jakub Adamski <kuba@exemplum.pl>
Date: Wed, 5 May 2021 22:07:54 +0200
Subject: [PATCH] zad5-update

---
 zajecia5/zadania.R | 134 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 134 insertions(+)

diff --git a/zajecia5/zadania.R b/zajecia5/zadania.R
index 9666e6a..8ad7817 100644
--- a/zajecia5/zadania.R
+++ b/zajecia5/zadania.R
@@ -32,7 +32,141 @@ rev(1 / lambda_limits^2)
 
 # ZAD 3
 
+median_cint <- function(x, conf_level = 0.95) {
+  m <- mean(x^2)
+  a <- 1 - conf_level
+  n <- length(x)
+  L <- sqrt(log(2) * m * (1 - qnorm(1 - a / 2) / sqrt(n)))
+  R <- sqrt(log(2) * m * (1 + qnorm(1 - a / 2) / sqrt(n)))
+  w <- list(title = "mediana", est = sqrt(log(2) * m), l = L, r = R, conf_level = conf_level)
+  class(w) <- "confint"
+  return(w)
+}
+
+
+print.confint <- function(x) {
+  cat(x$conf_level * 100, "percent confidence interval:", "\n")
+  cat(x$l, " ", x$r, "\n")
+}
+
+summary.confint <- function(x) {
+  cat("\n", "Confidence interval of", x$title, "\n", "\n")
+  cat(x$conf_level * 100, "percent confidence interval:", "\n")
+  cat(x$l, " ", x$r, "\n")
+  cat("sample estimate", "\n")
+  cat(x$est, "\n")
+}
 
 
 
+x <- c(0.9, 6.2, 2.1, 4.1, 7.3, 
+       1.0, 4.6, 6.4, 3.8, 5.0, 
+       2.7, 9.2, 5.9, 7.4, 3.0, 
+       4.9, 8.2, 5.0, 1.2, 10.1,
+       12.2, 2.8, 5.9, 8.2, 0.5)
+median_cint(x)
+summary(median_cint(x))
 
+
+# ZAD 4
+
+conf_int <- function(x, conf_level = 0.95) {
+  c(mean(x) - sd(x) * qt(1 - (1 - conf_level) / 2, length(x) - 1) / sqrt(length(x)), 
+    mean(x) + sd(x) * qt(1 - (1 - conf_level) / 2, length(x) - 1) / sqrt(length(x)))
+}
+
+mu <- 1
+sigma <- 3
+nr <- 1000
+df <- 3
+lambda <- 3
+
+n <- 10
+cat(paste("n = ", n, sep = ""), "\n")
+
+temp <- numeric(nr)
+set.seed(1234)
+for (i_nr in seq_len(nr)) {
+  x <- rnorm(n, mu, sigma)
+  temp_int <- conf_int(x)
+  temp[i_nr] <- ((temp_int[1] < mu) & (mu < temp_int[2]))
+}
+mean(temp)
+
+temp <- numeric(nr)
+set.seed(1234)
+for (i_nr in seq_len(nr)) {
+  x <- rchisq(n, df)
+  temp_int <- conf_int(x)
+  temp[i_nr] <- ((temp_int[1] < df) & (df < temp_int[2]))
+}
+mean(temp)
+
+temp <- numeric(nr)
+set.seed(1234)
+for (i_nr in seq_len(nr)) {
+  x <- rexp(n, rate = lambda)
+  temp_int <- conf_int(x)
+  temp[i_nr] <- ((temp_int[1] < 1 / lambda) & (1 / lambda < temp_int[2]))
+}
+mean(temp)
+
+n <- 50
+cat(paste("n = ", n, sep = ""), "\n")
+
+temp <- numeric(nr)
+set.seed(1234)
+for (i_nr in seq_len(nr)) {
+  x <- rnorm(n, mu, sigma)
+  temp_int <- conf_int(x)
+  temp[i_nr] <- ((temp_int[1] < mu) & (mu < temp_int[2]))
+}
+mean(temp)
+
+temp <- numeric(nr)
+set.seed(1234)
+for (i_nr in seq_len(nr)) {
+  x <- rchisq(n, df)
+  temp_int <- conf_int(x)
+  temp[i_nr] <- ((temp_int[1] < df) & (df < temp_int[2]))
+}
+mean(temp)
+
+temp <- numeric(nr)
+set.seed(1234)
+for (i_nr in seq_len(nr)) {
+  x <- rexp(n, rate = lambda)
+  temp_int <- conf_int(x)
+  temp[i_nr] <- ((temp_int[1] < 1 / lambda) & (1 / lambda < temp_int[2]))
+}
+mean(temp)
+
+n <- 100
+cat(paste("n = ", n, sep = ""), "\n")
+
+temp <- numeric(nr)
+set.seed(1234)
+for (i_nr in seq_len(nr)) {
+  x <- rnorm(n, mu, sigma)
+  temp_int <- conf_int(x)
+  temp[i_nr] <- ((temp_int[1] < mu) & (mu < temp_int[2]))
+}
+mean(temp)
+
+temp <- numeric(nr)
+set.seed(1234)
+for (i_nr in seq_len(nr)) {
+  x <- rchisq(n, df)
+  temp_int <- conf_int(x)
+  temp[i_nr] <- ((temp_int[1] < df) & (df < temp_int[2]))
+}
+mean(temp)
+
+temp <- numeric(nr)
+set.seed(1234)
+for (i_nr in seq_len(nr)) {
+  x <- rexp(n, rate = lambda)
+  temp_int <- conf_int(x)
+  temp[i_nr] <- ((temp_int[1] < 1 / lambda) & (1 / lambda < temp_int[2]))
+}
+mean(temp)