rtgin {ginormal}

Generating random numbers from the generalized inverse normal distribution truncated to the positive or negative reals

Description

Generating random numbers from the generalized inverse normal distribution truncated to the positive or negative reals

Usage

rtgin(
  size,
  alpha,
  mu,
  tau,
  sign,
  algo = "hormann",
  method = "Fortran",
  verbose = FALSE
)

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.

sign

logical. TRUE implies truncation to positive numbers (z > 0) and FALSE to negative numbers (z < 0).

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.

verbose

logical; should the acceptance rate from the ratio-of-uniforms method be provided along with additional information? Defaults to FALSE.

Details

Currently, only values of alpha > 2 are supported. For Bayesian posterior sampling, alpha is always larger than 2 even for non-informative priors. Generate from positive region (z > 0) hen sign = TRUE, and from negative region (z < 0) when sign = FALSE. When verbose = TRUE, a list is returned containing the actual draw in value, as well as average acceptance rate avg_arate and total number of acceptance-rejection steps ARiters.

Value

If verbose = FALSE (default), a numeric vector of length size. Otherwise, a list with components value, avg_arate, and ARiters

Examples

# Generate 1000 values from the truncated distributions with alpha = 5, mu = 0, tau = 1
set.seed(123456)
n_draws <- 1000
z_p <- rtgin(n_draws, 5, 0, 1, TRUE)
z_n <- rtgin(n_draws, 5, 0, 1, FALSE)

# Compare generation from truncation to positive reals with true density
n_values <- 200
z_vals <- seq(-5, 5, length.out = n_values)
fz_p <- sapply(z_vals[z_vals > 0], function(z) dtgin(z, 5, 0, 1, TRUE, FALSE))
fz_p <- c(rep(0, n_values - sum(z_vals > 0)), fz_p)
temp <- hist(z_p, breaks = 100, plot = FALSE)
plot(temp, freq = FALSE, xlim = c(-5, 5), ylim = range(c(fz_p, temp$density)),
     main = '', xlab = 'Values', ylab = 'Density', col = 'blue')
lines(z_vals, fz_p, col = 'red', lwd = 2)

# Compare generation from truncation to negative reals with true density
fz_n <- sapply(z_vals[z_vals < 0], function(z) dtgin(z, 5, 0, 1, FALSE, FALSE))
fz_n <- c(fz_n, rep(0, n_values - sum(z_vals < 0)))
temp <- hist(z_n, breaks = 100, plot = FALSE)
plot(temp, freq = FALSE, xlim = c(-5, 5), ylim = range(c(fz_n, temp$density)),
     main = '', xlab = 'Values', ylab = 'Density', col = 'blue')
lines(z_vals, fz_n, col = 'red', lwd = 2)

# verbose = TRUE provides info on the acceptance rate of the
# ratio-of-uniforms acceptance-rejection method for sampling the variables
draw_list <- rtgin(50, 5, 0, 1, sign = TRUE, verbose = TRUE)
draw_list$ARiters      # Acceptance-Rejection iterations
draw_list$avg_arate    # Average of 1/ARiters