fBasics (version 4021.93)

nig: Normal Inverse Gaussian Distribution

Description

Density, distribution function, quantile function and random generation for the normal inverse Gaussian distribution.

Usage

dnig(x, alpha = 1, beta = 0, delta = 1, mu = 0, log = FALSE)
pnig(q, alpha = 1, beta = 0, delta = 1, mu = 0)
qnig(p, alpha = 1, beta = 0, delta = 1, mu = 0)
rnig(n, alpha = 1, beta = 0, delta = 1, mu = 0)

Value

dnig gives the density,

pnig gives the distribution function,

qnig gives the quantile function, and

rnig generates random deviates.

Each function returns a numeric vector with attribute "param"

containing the parameters of the distribution.

GNB TODO: It seems that only rnig has an attribute and that is called "control" (but it indeed contains the parameters).

Arguments

x,q

a numeric vector of quantiles.

p

a numeric vector of probabilities.

n

number of observations.

alpha

shape parameter.

beta

skewness parameter beta, abs(beta) is in the range (0, alpha).

delta

scale parameter, must be zero or positive.

mu

location parameter, by default 0.

log

a logical flag by default FALSE. Should labels and a main title be drawn to the plot?

Author

David Scott for code implemented from R's contributed package HyperbolicDist.

Details

The parameters alpha, beta, delta, mu are in the first parameterization of the distribution.

The random deviates are calculated with the method described by Raible (2000).

References

Atkinson, A.C. (1982); The simulation of generalized inverse Gaussian and hyperbolic random variables, SIAM J. Sci. Stat. Comput. 3, 502--515.

Barndorff-Nielsen O. (1977); Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. Lond., A353, 401--419.

Barndorff-Nielsen O., Blaesild, P. (1983); Hyperbolic distributions. In Encyclopedia of Statistical Sciences, Eds., Johnson N.L., Kotz S. and Read C.B., Vol. 3, pp. 700--707. New York: Wiley.

Raible S. (2000); Levy Processes in Finance: Theory, Numerics and Empirical Facts, PhD Thesis, University of Freiburg, Germany, 161 pages.

Examples

## nig -
   set.seed(1953)
   r = rnig(5000, alpha = 1, beta = 0.3, delta = 1)
   plot(r, type = "l", col = "steelblue",
     main = "nig: alpha=1 beta=0.3 delta=1")
 
## nig - 
   # Plot empirical density and compare with true density:
   hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue")
   x = seq(-5, 5, 0.25)
   lines(x, dnig(x, alpha = 1, beta = 0.3, delta = 1))
 
## nig -  
   # Plot df and compare with true df:
   plot(sort(r), (1:5000/5000), main = "Probability", col = "steelblue")
   lines(x, pnig(x, alpha = 1, beta = 0.3, delta = 1))
   
## nig -
   # Compute Quantiles:
   qnig(pnig(seq(-5, 5, 1), alpha = 1, beta = 0.3, delta = 1), 
     alpha = 1, beta = 0.3, delta = 1)