powdist (version 0.1.4)

ReversalPowerT: The Power Reversal Student t Distribution

Description

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

Usage

drpt(x, lambda = 1, mu = 0, sigma = 1, df, log = FALSE)
prpt(q, lambda = 1, mu = 0, sigma = 1, df, lower.tail = TRUE,
  log.p = FALSE)
qrpt(p, lambda = 1, mu = 0, sigma = 1, df, lower.tail = TRUE,
  log.p = FALSE)
rrpt(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 reversal 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.

Examples

# NOT RUN {
drpt(1, 1, 3, 4, 1)
prpt(1, 1, 3, 4, 1)
qrpt(0.2, 1, 3, 4, 1)
rrpt(5, 2, 3, 4, 1)
# }