ugarchdist: Distribution: rgarch distribution functions
In rgarch: Flexible GARCH modelling in R

Description Usage Arguments Details Value Author(s) References

Density, distribution function, quantile function, random generation and fitting from the univariate distributions implemented in the rgarch package, with functions for skewness and excess kurtosis given density skew and shape parameters.

`rgarchdist`	rgarch univariate distributions,
`fitdist`	MLE parameter fit for the rgarch univariate distributions,

ddist(distribution = "norm", y, mu = 0, sigma = 1, lambda = -0.5, skew = 1, shape = 5)
pdist(distribution = "norm", q, mu = 0, sigma = 1, lambda = -0.5, skew = 1, shape = 5)
qdist(distribution = "norm", p, mu = 0, sigma = 1, lambda = -0.5, skew = 1, shape = 5)
rdist(distribution = "norm", n, mu = 0, sigma = 1, lambda = -0.5, skew = 1, shape = 5)
fitdist(distribution = "norm", x, control=list())
dskewness(distribution = "norm", skew = 1, shape = 5, lambda = -0.5)
dkurtosis(distribution = "norm", skew = 1, shape = 5, lambda = -0.5)

`distribution`	The distribution name. Valid choices are “norm”, “snorm”, “std”, “sstd”, “ged”, “sged”, “nig”, “jsu”.
`mu, sigma, skew, shape`	location, scale and skewness and shape parameters (see details).
`lambda`	The additional shape parameter for the Generalized Hyperbolic and NIG distributions.
`n`	the number of observations.
`p`	a numeric vector of probabilities.
`y, q`	a numeric vector of quantiles.
`x`	a univariate dataset (for fitting routine).
`control`	control parameters passed to the `solnp` solver.

For the dQuotenig and “ghyp” distributions, the shape, skew and lambda are transformed from the ‘zeta-rho’ to the ‘alpha-beta’ parametrization and then scaled by the mean and standard deviation. The fitting routines use the solnp solver and minimize the negative of the log-likelihood. The “dskewness” and “dkurtosis” functions take as inputs the distribution name, skew and shape parameters and return the skewneness and excess kurtosis of the distribution. Currently, the skewness and kurtosis of the JSU distribution are not yet implemented. Also the function are not at present vectorized.

d* returns the density, p* returns the distribution function, q* returns the quantile function, and r* generates random deviates,
all values are numeric vectors.

fitdist returns a list with the following components:

`par`	The best set of parameters found.
`value`	The likelihood values of the optimization (vector whose length represents the number of major iterations).
`convergence`	An integer code. 0 indicates successful convergence.
`lagrange`	The lagrange multiplier value at convergence.
`h`	The hessian at the solution.
`xineq0`	The value of the inequality constraint multipluer (NULL for the distribution fit problems).

dskewness returns the skewness of the distribution. dkurtosis returns the excess kurtosis of the distribution.

Diethelm Wuertz for the Rmetrics R-port of the “norm”, “snorm”, “std”, “sstd”, “ged”, “sged” and “nig” distrbutions.
Rigby, R. A. and Stasinopoulos D. M for the JSU distribution in the gamlss package.
Alexios Ghalanos for rgarch implementation and higher moment distribution functions.

Johnson, N. L. Systems of frequency curves derived from the first law of Laplace ,1954, Trabajos de Estadistica, 5, 283-291.
Barndorff-Nielsen, O. E.Normal inverse Gaussian processes and the modeling of stock returns, 1995, Rep. No. 300, Dept. of Theor. Stat., Inst. of Math., Univ. of Aarhus, Denmark.
Fernandez C. and Steel, M.F.J. On Bayesian Modelling of Fat Tails and Skewness, 2000, Preprint, 31 pages.

rgarch documentation built on May 2, 2019, 5:22 p.m.