# dist-nig: Normal Inverse Gaussian Distribution In fBasics: Rmetrics - Markets and Basic Statistics

## Description

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

## Usage

 ```1 2 3 4``` ```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) ```

## Arguments

 `alpha, beta, delta, mu` shape parameter `alpha`; skewness parameter `beta`, `abs(beta)` is in the range (0, alpha); scale parameter `delta`, `delta` must be zero or positive; location parameter `mu`, by default 0. These are the parameters in the first parameterization. `log` a logical flag by default `FALSE`. Should labels and a main title drawn to the plot? `n` number of observations. `p` a numeric vector of probabilities. `x, q` a numeric vector of quantiles.

## Details

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

## Value

All values for the `*nig` functions are numeric vectors: `d*` returns the density, `p*` returns the distribution function, `q*` returns the quantile function, and `r*` generates random deviates.

All values have attributes named `"param"` listing the values of the distributional parameters.

## Author(s)

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

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ``` ## 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) ```

fBasics documentation built on Nov. 18, 2017, 4:05 a.m.