PowerT {powdist}

The Power Student t Distribution

Description

Density, distribution function, quantile function and random generation for the power Student t distribution with parameters mu, sigma, lambda and df.

Usage

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

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

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

rpt(n, lambda = 1, mu = 0, sigma = 1, df)

Arguments

x, q

vector of quantiles.

lambda

shape parameter.

mu, sigma

location and scale parameters.

df

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

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.

Details

The power Student t distribution has density

f(x)=[\lambda/\sigma][f((x-\mu)/\sigma)][F((x-\mu)/\sigma)] ^(\lambda-1),

where -\infty<\mu<\infty is the location paramether, \sigma^2>0 the scale parameter and \lambda>0 the shape parameter.

References

Lemonte A. and Bazán J.L.

Examples

dpt(1, 1, 3, 4, 1)
ppt(1, 1, 3, 4, 1)
qpt(0.2, 1, 3, 4, 1)
rpt(5, 2, 3, 4, 1)