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# Random variate generation from Laplace distribution
rlapl <- function(n, mu, lambda) {
u <- runif(n)
cond <- (u >= 0.5)
rand <- mu + (-1)^cond * lambda * log(2 * (cond + (-1)^cond * u))
return(rand)
}
# Probability density function (pdf) of Laplace distribution
dlapl <- function(x, mu = 0, lambda = 1) {
pdf <- 1 / (2 * lambda) * exp(-abs(x - mu) / lambda)
return(pdf)
}
# Cumulative distribution function (cdf) of Laplace distribution
plapl = function(x, mu = 0, lambda = 1) {
cond <- (x >= mu)
cdf <- cond + (-1)^cond*0.5 * exp(-abs(x - mu) / lambda)
return(cdf)
}
# Log-likelihood (normal error)
#' @importFrom stats pnorm
llik.n <- function(a, s, x) {
n <- length(x)
return(-n * log(2 * a) + sum(log(pnorm((x + a) / s) - pnorm((x - a) / s))))
}
#' @importFrom stats pnorm
llik.n2 = function(t, x) {
n <- length(x)
a <- t[1]
s <- t[2]
return (-n * log(2 * a) + sum(log(pnorm((x + a) / s)-pnorm((x - a) / s))))
}
# The function whose zeros are endpoints of LR confidence interval (normal
# error)
#' @importFrom stats qchisq
fun.cin <- function(a, ml, x, s, cl) {
-llik.n(a, s, x) + llik.n(ml, s, x) - 0.5 * qchisq(cl, 1)
}
# The integrand appearing in the Fisher information (normal error)
#' @importFrom stats dnorm
#' @importFrom stats pnorm
int.n <- function(x, alfa) {
(dnorm(x + alfa) + dnorm(x - alfa))^2 / (pnorm(x - alfa, lower.tail = F) -
pnorm(x + alfa, lower.tail = F))
}
# Log-likelihood (Laplace error)
llik.l = function(a, l, x) {
n <- length(x)
return(-n * log(2 * a) + sum(log(plapl((x + a) / l) - plapl((x - a) / l))))
}
llik.l2 = function(t, x) {
n <- length(x)
a <- t[1]
l <- t[2]
return(-n * log(2 * a) + sum(log(plapl((x + a) / l) - plapl((x - a) / l))))
}
# The function whose zeros are endpoints of LR confidence interval (Laplace
# error)
#' @importFrom stats qchisq
fun.cil <- function(a, ml, x, l, cl) {
-llik.l(a, l, x) + llik.l(ml, l, x) - 0.5 * qchisq(cl, 1)
}
# The integrand appearing in the Fisher information (Laplace error)
int.l <- function(x, alfa) {
(dlapl(x + alfa) + dlapl(x - alfa))^2/(plapl(x + alfa) - plapl(x - alfa))
}
# Log-likelihood (scaled Student error with df = 5)
#' @importFrom stats pt
llik.s = function(a, s, x) {
n <- length(x)
return(-n * log(2 * a) + sum(log(pt((x + a) / s, 5) - pt((x - a) / s, 5))))
}
#' @importFrom stats pt
llik.s2 = function(t, x) {
n <- length(x)
a <- t[1]
s <- t[2]
return(-n * log(2 * a) + sum(log(pt((x + a) / s, 5) - pt((x - a) / s, 5))))
}
# The function whose zeros are endpoints of LR confidence interval (Student
# error)
#' @importFrom stats qchisq
fun.cis <- function(a, ml, x, s, cl) {
-llik.s(a, s, x) + llik.s(ml, s, x) - 0.5 * qchisq(cl, 1)
}
# The integrand appearing in the Fisher information (Student error)
#' @importFrom stats dt
#' @importFrom stats pt
int.s <- function(x, alfa) {
(dt(x + alfa, 5) + dt(x - alfa, 5))^2/(pt(x + alfa, 5) - pt(x - alfa, 5))
}
# Log-likelihood (scaled Student error with df = 4, 3, 2, 1)
llik.st = function(a, s, df, x) {
n <- length(x)
return(-n * log(2*a) + sum(log(pt((x + a) / s, df) - pt((x - a)/s, df))))
}
llik.st2 = function(t, df, x) {
n <- length(x)
a <- t[1]
s <- t[2]
return(-n * log(2 * a) + sum(log(pt((x + a) / s, df) - pt((x - a) / s, df))))
}
## Funkcija za odredjivanje intervala povjerenja (Student error, 4, 3, 2, 1)
fun.cist <- function(a, ml, x, s, df, cl) {
-llik.st(a, s, df, x) + llik.st(ml, s, df, x) - 0.5 * qchisq(cl, 1)
}
## podintegralna f-ja iz as. var
int.st <- function(x, df, alfa) {
(dt(x + alfa, df) + dt(x - alfa, df))^2 / (pt(x + alfa, df) -
pt(x - alfa, df))
}
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