ginormal (version 0.0.2)

rgin: Generating random numbers from the generalized inverse normal distribution

Description

Generating random numbers from the generalized inverse normal distribution

Usage

rgin(size, alpha, mu, tau, algo = "hormann", method = "Fortran")

Value

Numeric vector of length size.

Arguments

size

number of desired draws. Output is numpy vector of length equal to size.

alpha

degrees-of-freedom parameter.

mu

similar to location parameter, controls asymmetry of the distribution.

tau

similar to scale parameter, controls spread of the distribution.

algo

string with desired algorithm to compute minimal bounding rectangle. If "hormann", use the method from Hörmann and Leydold (2014). When "leydold", use the one from Leydold (2001). Defaults to "hormann" and returns an error for any other values.

method

string with the method used to compute the parabolic cylinder function in the normalization constant. method = "Fortran" uses a compiled Fortran version, which is the default. method = "R" uses an R translation of this function.

Details

Currently, only values of alpha > 2 are supported. For Bayesian posterior sampling, alpha is always larger than 2 even for non-informative priors. The algorithm requires calculating the probability of truncation region (either z < 0 or z > 0). It is more stable to compute a probability bounded away from 0. As mu controls asymmetry, when mu > 0, P(truncation region) = P(z > 0) >= 50%, and this probability is computed. If mu < 0, P(z < 0) >= 50% and this region's probability is used.

Examples

# Generate 1000 values from the distribution with alpha = 5, mu = 0, tau = 1
set.seed(123456)
z_unc <- rgin(1000, 5, 0, 1)

# Compare histogram to true density
z_vals <- seq(-5, 5, length.out = 200)
fz_unc <- sapply(z_vals, function(z) dgin(z, 5, 0, 1, FALSE))
temp <- hist(z_unc, breaks = 200, plot = FALSE)
plot(temp, freq = FALSE, xlim = c(-5, 5), ylim = range(c(fz_unc, temp$density)),
     main = '', xlab = 'Values', ylab = 'Density', col = 'blue')
lines(z_vals, fz_unc, col = 'red', lwd = 2)