neodistr (version 0.1.2)

fossep: 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)

Value

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

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.

Author

Almira Utami

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: $$f(x |\mu,\sigma,\beta,\alpha) = \frac{c}{\sigma} \exp \left( - \frac{1}{2} \left| v z \right|^\tau \right) \quad \text{if } x < \mu$$ $$f(x |\mu,\sigma,\beta,\alpha) = \frac{c}{\sigma} \exp \left( - \frac{1}{2} \left| \frac{v}{z} \right|^\tau \right) \quad \text{if } x \ge \mu$$ $$ \text{where } -\infty < y < \infty, \ -\infty < \mu < \infty, \ \sigma > 0, \ \alpha > 0, \ \beta > 0$$ $$ z = \frac{x - \mu}{\sigma}$$ $$ c = v \tau \left[ (1 + v^2) 2^{\frac{1}{\tau}} \Gamma \left( \frac{1}{\tau} \right) \right]^{-1}$$

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)