LocationScaleT function

Location-scale version of the t-distribution

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).

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.

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)

See Also

TDist