Student-t Distribution
Functions to compute density, distribution function, quantile function and to generate random variates for the Student-t distribution.
dstd(x, mean = 0, sd = 1, nu = 5, log = FALSE) pstd(q, mean = 0, sd = 1, nu = 5) qstd(p, mean = 0, sd = 1, nu = 5) rstd(n, mean = 0, sd = 1, nu = 5)
mean, sd, nu |
location parameter |
n |
the number of observations. |
p |
a numeric vector of probabilities. |
x, q |
a numeric vector of quantiles. |
log |
a logical; if TRUE, densities are given as log densities. |
d* returns the density,
p* returns the distribution function,
q* returns the quantile function, and
r* generates random deviates,
all values are numeric vectors.
Diethelm Wuertz for the Rmetrics R-port.
Fernandez C., Steel M.F.J. (2000); On Bayesian Modelling of Fat Tails and Skewness, Preprint, 31 pages.
## std -
par(mfrow = c(2, 2))
set.seed(1953)
r = rstd(n = 1000)
plot(r, type = "l", main = "sstd", col = "steelblue")
# Plot empirical density and compare with true density:
hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue")
box()
x = seq(min(r), max(r), length = 201)
lines(x, dstd(x), lwd = 2)
# Plot df and compare with true df:
plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue",
ylab = "Probability")
lines(x, pstd(x), lwd = 2)
# Compute quantiles:
round(qstd(pstd(q = seq(-1, 5, by = 1))), digits = 6)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.