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100644 --- a/zajecia5/.Rhistory +++ b/zajecia5/.Rhistory @@ -0,0 +1,137 @@ +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)