integrate density in logit space and split by component such that the quantile function of each component is used. This ensures that the R implementation of the quantile function is always used.
integrate_density_log(
log_integrand,
mix,
Lplower = -Inf,
Lpupper = Inf,
eps = 1e-09
)
function to integrate over which must return the log(f)
density over which to integrate
logit of lower cumulative density
logit of upper cumulative density