PowerT: The Power Student t Distribution

Description Usage Arguments Details References Examples

Description

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

Usage

1
2
3
4
5
6
7
8
9
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

1
2
3
4
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.