# 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.

TDist

## Examples

# 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)

# }