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I fitted a GB2 distribution to my income data and then got puzzled when examining the parameter estimates. I observed that for parameters similar to c(809.6687, 116.4727, 0.0342, 0.0278), the quantile values returned by qGB2 are somewhat strange. For instance, the 10% Percentile is still 0 which does not make sense to me, in particular when having a look at the associated density function. Also, using the random number generator rGB2 many 0 values are drawn from the distribution.

I compared the results to the ones by the GB2 R package. Here, the quantile values look more reasonable to me for the very same set of GB2 parameters. For standard GB2 parameters, the two packages return identical results but not for some extreme parameter values. Why is that and might this be a potential bug in the gamlss.dist package?

Here, my example code:

##### GB2 Distribution #####

rm(list = ls())

set.seed(79)

library(GB2)
library(gamlss.dist)

params = c(809.6687, 116.4727, 0.0342, 0.0278)
# params = c(1, 1, 1, 0.5)
mu = params[1]
sigma = params[2]
nu = params[3]
tau = params[4]

GB2::qgb2(c(0.1, 0.5, 0.9), shape1 = sigma, scale = mu, shape2 = nu, shape3 = tau)
gamlss.dist::qGB2(c(0.1, 0.5, 0.9), mu = mu, sigma = sigma, nu = nu, tau = tau)

GB2::pgb2(c(10, 100, 1000, 10000), shape1 = sigma, scale = mu, shape2 = nu, shape3 = tau)
gamlss.dist::pGB2(c(10, 100, 1000, 10000), mu = mu, sigma = sigma, nu = nu, tau = tau)

GB2::dgb2(c(10, 100, 1000, 10000), shape1 = sigma, scale = mu, shape2 = nu, shape3 = tau)
gamlss.dist::dGB2(c(10, 100, 1000, 10000), mu = mu, sigma = sigma, nu = nu, tau = tau)


r1 = GB2::rgb2(100000, shape1 = sigma, scale = mu, shape2 = nu, shape3 = tau)
summary(r1)
sum(r1 == 0)
r2 = gamlss.dist::rGB2(100000, mu = mu, sigma = sigma, nu = nu, tau = tau)
summary(r2)
sum(r2 == 0)

I've found an issue with the BCCG distribution functions. They don't gracefully handle missing values due to the use of any(q < 0), which will return NA if any of its inputs are missing. Here's a reprex, and a comparison to the behaviour of pnorm, which behaves as expected:

# quantiles
q1 = c(0,1)
q2 = c(0,1,NA_real_)

# Expected output: 2 numbers
gamlss.dist::pBCCG(q1, mu = 1, sigma = 1, nu = 0)
#> [1] 0.0 0.5
pnorm(q1, 1, 0.5)
#> [1] 0.02275013 0.50000000

# Expected output: 2 numbers and a missing value. pnorm does this,
# but pBCCG returns an error
gamlss.dist::pBCCG(q2, mu = 1, sigma = 1, nu = 0)
#> Error in if (any(q < 0)) stop(paste("q must be positive", "\n", "")): missing value where TRUE/FALSE needed
pnorm(q2, mean = 1, sd = 0.5)
#> [1] 0.02275013 0.50000000         NA

^{Created on 2023-09-14 with reprex v2.0.2}