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# Density of the skewed-t distribution - Fernandez and Steel (1998)
dst <- function (x, a = 0, b = 1, skew = 1, df = 10, log = FALSE) {
if (log) {
lnumerator <- log(2) - log(skew + 1 / skew)
ldenom1 <- lbeta(0.5, df / 2) + log(b) + log(df) / 2
ldenom2 <- (df + 1) * log(1 + (x - a)^2 /
(skew^(2 * sign(x - a)) * df * b^2)) / 2
out <- lnumerator - ldenom1 - ldenom2
} else {
numerator <- 2 / (skew + 1 / skew)
denom1 <- beta(0.5, df / 2) * b * sqrt(df)
denom2 <- (1 + (x - a)^2 /
(skew^(2 * sign(x - a)) * df * b^2))^((df + 1) / 2)
out <- numerator / (denom1 * denom2)
}
return(out)
}
# log-likelihood of the skew-t distribution of Fernandez and Steel (1998)
# theta = c(a, b, skew, df)
loglikST <- function(theta, x) {
dst(
x, a = theta[1], b = theta[2], skew = theta[3], df = theta[4], log = TRUE
) %>%
sum() %>%
max(-.Machine$double.xmax, na.rm = TRUE) %>%
return()
}
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