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)

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.

# NOT RUN { 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) # }