PowerT: The Power Student t Distribution

In powdist: Power and Reversal Power Distributions

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 ≤ x ], otherwise, P[X > x].
p	vector of probabilities.
n	number of observations.

Details

The power Student t distribution has density

f(x)=[λ/σ][f((x-μ)/σ)][F((x-μ)/σ)] ^(λ-1),

where -∞<μ<∞ is the location paramether, σ^2>0 the scale parameter and λ>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)

Example output

[1] 0.06366198
[1] 0.3524164
[1] -2.505528
[1]  2.9198734  2.0346696 30.1499991  5.9767464  0.7024134

powdist documentation built on May 1, 2019, 10:11 p.m.