Student-t Distribution

Description

Functions to compute density, distribution function, quantile function and to generate random variates for the Student-t distribution.

Usage

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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)

Arguments

mean, sd, nu

location parameter mean, scale parameter sd, shape parameter nu.

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.

Value

d* returns the density, p* returns the distribution function, q* returns the quantile function, and r* generates random deviates,
all values are numeric vectors.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

References

Fernandez C., Steel M.F.J. (2000); On Bayesian Modelling of Fat Tails and Skewness, Preprint, 31 pages.

Examples

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## 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)

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