fossep: Fernandez-Osiewalski-Steel Skew Exponential Power...

In neodistr: Neo-Normal Distribution

Fernandez-Osiewalski-Steel Skew Exponential Power Distribution

Description

To calculate density function, distribution function, quantile function, and build data from random generator function for the Fernandez-Osiewalski-Steel Skew Exponential Power Distribution.

Usage

dfossep(x, mu = 0, sigma = 1, alpha = 2, beta = 2, log = FALSE)

pfossep(
  q,
  mu = 0,
  sigma = 1,
  alpha = 2,
  beta = 2,
  lower.tail = TRUE,
  log.p = FALSE
)

qfossep(
  p,
  mu = 0,
  sigma = 1,
  alpha = 2,
  beta = 2,
  lower.tail = TRUE,
  log.p = FALSE
)

rfossep(n, mu = 0, sigma = 1, alpha = 2, beta = 2)

Arguments

x, q	vector of quantiles.
mu	a location parameter.
sigma	a scale parameter.
alpha	a shape parameter (skewness).
beta	a shape parameter (kurtosis).
log, log.p	logical; if TRUE, probabilities p are given as log(p) The default value of this parameter is FALSE
lower.tail	logical;if TRUE (default), probabilities are P\left[ X\leq x\right], otherwise, P\left[ X>x\right] .
p	vectors of probabilities.
n	number of observations.

Details

Fernandez-Osiewalski-Steel Skew Exponential Power Distribution

The Fernandez-Osiewalski-Steel Skew Exponential Power distribution with parameters \mu, \sigma,\alpha, and \beta has density:

f(x |\mu,\sigma,\beta,\alpha) = \frac{c}{\sigma} \exp \left( - \frac{1}{2} \left| v z \right|^\tau \right) \quad \text{if } x < \mu

f(x |\mu,\sigma,\beta,\alpha) = \frac{c}{\sigma} \exp \left( - \frac{1}{2} \left| \frac{v}{z} \right|^\tau \right) \quad \text{if } x \ge \mu

\text{where } -\infty < y < \infty, \ -\infty < \mu < \infty, \ \sigma > 0, \ \alpha > 0, \ \beta > 0

z = \frac{x - \mu}{\sigma}

c = v \tau \left[ (1 + v^2) 2^{\frac{1}{\tau}} \Gamma \left( \frac{1}{\tau} \right) \right]^{-1}

Value

dfossep gives the density , pfossep gives the distribution function, qfossep gives quantiles function, rfossep generates random numbers.

Author(s)

Almira Utami

References

Fernandez, C., Osiewalski, J., & Steel, M. F. (1995) Modeling and inference with v-spherical distributions. Journal of the American Statistical Association, 90(432), pp 1331-1340.

Rigby, R.A. and Stasinopoulos, M.D. and Heller, G.Z. and De Bastiani, F. (2019) Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R.CRC Press

Examples

dfossep(4, mu=0, sigma=1, alpha=2, beta=2)
pfossep(4, mu=0, sigma=1, alpha=2, beta=2)
qfossep(0.4, mu=0, sigma=1, alpha=2, beta=2)
rfossep(4, mu=0, sigma=1, alpha=2, beta=2)

neodistr documentation built on Aug. 8, 2025, 7:35 p.m.