# Density for the generalized inverse normal distribution truncated to the positive or negative reals ```r 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. ## Returns Numeric scalar with density. ## 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. ## Examples ```r # 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) ```

dtgin function