dtgin {ginormal}

Density for the generalized inverse normal distribution truncated to the positive or negative reals

Description

Density for the generalized inverse normal distribution truncated to the positive or negative reals

Usage

dtgin(
  z,
  alpha,
  mu,
  tau,
  sign = TRUE,
  log = TRUE,
  quasi = FALSE,
  method = "Fortran"
)

Arguments

z

quantile.

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).

log

logical; should the log of the density be returned? Defaults to TRUE.

quasi

logical; should the quasi-density value be returned? Defaults to FALSE.

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 scalars are supported for the quantile and parameter values. Density is supported on the positive reals (z > 0) when sign = TRUE and to negative reals (z < 0) when sign = FALSE. mu can take any value in (-\infty, \infty). Density is only defined for parameter values alpha > 1 or tau > 0, so it is set to 0 outside of these values. The quasi-density or kernel is the density without the normalization constant, use quasi = TRUE for this behavior.

Value

Numeric scalar with density.

Examples

# Computing (log) truncated densities
dtgin(z = 1, alpha = 3, mu = 1, tau = 1, sign = TRUE, log = TRUE, quasi = FALSE)
dtgin(z = -1, alpha = 3, mu = -1, tau = 1, sign = FALSE, log = TRUE, quasi = FALSE)

# Generalized inverse normal density with alpha = 5, mu = 0, tau = 1
n_values <- 200
z_vals <- seq(-5, 5, length.out = n_values)

# Truncated to positive reals (z > 0)
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)
plot(z_vals, fz_p, type = "l", xlab = 'Values', ylab = 'Density')

# Truncated to positive reals (z < 0)
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)))
plot(z_vals, fz_n, type = "l", xlab = 'Values', ylab = 'Density')

# Both truncated densities together
plot(z_vals, fz_p, type = "l", xlab = 'Values', ylab = 'Density')
lines(z_vals, fz_n, col = 'blue', lty = 2)
legend('topright', legend = c('z > 0', 'z < 0'),
       col = c('black', 'blue'), lty = 1:2)