extraDistr (version 1.10.0)

LocationScaleT: Location-scale version of the t-distribution

Description

Probability mass function, distribution function and random generation for location-scale version of the t-distribution. Location-scale version of the t-distribution besides degrees of freedom \(\nu\), is parametrized using additional parameters \(\mu\) for location and \(\sigma\) for scale (\(\mu = 0\) and \(\sigma = 1\) for standard t-distribution).

Usage

dlst(x, df, mu = 0, sigma = 1, log = FALSE)
plst(q, df, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qlst(p, df, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rlst(n, df, mu = 0, sigma = 1)

Arguments

x, q

vector of quantiles.

df

degrees of freedom (> 0, maybe non-integer). df = Inf is allowed.

mu

vector of locations

sigma

vector of positive valued scale parameters.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\).

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

See Also

TDist

Examples

x <- rlst(1e5, 1000, 5, 13)
hist(x, 100, freq = FALSE)
curve(dlst(x, 1000, 5, 13), -60, 60, col = "red", add = TRUE)
hist(plst(x, 1000, 5, 13))
plot(ecdf(x))
curve(plst(x, 1000, 5, 13), -60, 60, col = "red", lwd = 2, add = TRUE)