Standardized Normal Inverse Gaussian Distribution
dist-snig.Rd
Density, distribution function, quantile function and random generation for the standardized normal inverse Gaussian distribution.
Usage
dsnig(x, zeta = 1, rho = 0, log = FALSE)
psnig(q, zeta = 1, rho = 0)
qsnig(p, zeta = 1, rho = 0)
rsnig(n, zeta = 1, rho = 0)
Arguments
- x, q
a numeric vector of quantiles.
- p
a numeric vector of probabilities.
- n
number of observations.
- zeta
shape parameter
zeta
is positive.- rho
skewness parameter, a number in the range \((-1, 1)\).
- log
a logical flag by default
FALSE
. If TRUE, log values are returned.
Details
dsnig
gives the density,
psnig
gives the distribution function,
qsnig
gives the quantile function, and
rsnig
generates random deviates.
The random deviates are calculated with the method described by Raible (2000).
Examples
## snig -
set.seed(1953)
r = rsnig(5000, zeta = 1, rho = 0.5)
plot(r, type = "l", col = "steelblue",
main = "snig: zeta=1 rho=0.5")
## snig -
# Plot empirical density and compare with true density:
hist(r, n = 50, probability = TRUE, border = "white", col = "steelblue")
x = seq(-5, 5, length = 501)
lines(x, dsnig(x, zeta = 1, rho = 0.5))
## snig -
# Plot df and compare with true df:
plot(sort(r), (1:5000/5000), main = "Probability", col = "steelblue")
lines(x, psnig(x, zeta = 1, rho = 0.5))
## snig -
# Compute Quantiles:
qsnig(psnig(seq(-5, 5, 1), zeta = 1, rho = 0.5), zeta = 1, rho = 0.5)
#> [1] -5.000000e+00 -3.999999e+00 -2.999983e+00 -2.000011e+00 -1.000000e+00
#> [6] -2.609555e-07 1.000004e+00 2.000016e+00 3.000001e+00 4.000000e+00
#> [11] 5.000029e+00