diff --git a/zajecia5/.RData b/zajecia5/.RData
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Binary files /dev/null and b/zajecia5/.RData differ
diff --git a/zajecia5/.Rhistory b/zajecia5/.Rhistory
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+++ b/zajecia5/.Rhistory
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+load(url("http://ls.home.amu.edu.pl/data_sets/Centrala.RData"))
+library(EnvStats)
+epois(Centrala$Liczba,
+method = "mle/mme/mvue",
+ci = TRUE, ci.type = "two-sided", conf.level = 0.95,
+ci.method = "exact")$interval$limits
+epois(Centrala$Liczba,
+method = "mle/mme/mvue",
+ci = TRUE, ci.type = "two-sided", conf.level = 0.95,
+ci.method = "pearson.hartley.approx")$interval$limits
+epois(Centrala$Liczba,
+method = "mle/mme/mvue",
+ci = TRUE, ci.type = "two-sided", conf.level = 0.95,
+ci.method = "normal.approx")$interval$limits
+View(Centrala)
+awarie <- read.table("http://ls.home.amu.edu.pl/data_sets/awarie.txt")
+lambda_limits <- eexp(awarie$V1,
+method = "mle/mme",
+ci = TRUE, ci.type = "two-sided", conf.level = 0.95,
+ci.method = "exact")$interval$limits
+rev(1 / lambda_limits)
+rev(1 / lambda_limits^2)
+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))
+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)