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extraDistr (version 1.8.6)

NonStandardT: Non-standard t-distribution

Description

Probability mass function, distribution function and random generation for non-standard t-distribution. Non-standard 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

dnst(x, df, mu = 0, sigma = 1, log = FALSE)

pnst(q, df, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

qnst(p, df, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

rnst(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

Run this code

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

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