lumen provides density (d), CDF (p), quantile (q),
and random-generation (r) functions for several distributions
not covered by base R, plus moment (m) functions – mean and
variance – for those and for several distributions base R already
provides d-p-q-r for. A - marks a combination with no function.
Extreme value distributions
| Distribution | d-p-q-r | Moments |
| Generic extreme | dpqr-extreme | - |
| Gen. Extreme Value | dpqr-gev | mgev() |
| Gumbel | dpqr-gumbel | mgumbel() |
Gumbel, maximum of two | dpqr-gumbelx | - |
| Fréchet | dpqr-frechet | mfrechet() |
| Reverse Weibull | dpqr-revweibull | mrevweibull() |
| Reverse Gumbel | dpqr-revgumbel | mrevgumbel() |
| Order statistics | dpqr-order | - |
Order statistics have no quantile function (qorder() does not
exist). qrevgumbelExp() is a specialized quantile for the
exponential parametrization of the reverse Gumbel distribution, not a
general-purpose q slot – use qrevgumbel() for that.
Other distributions
| Distribution | d-p-q-r | Moments |
| Benford | dpqr-benford | mbenford() |
| Dirichlet | dpqr-dirichlet | - |
| Gompertz | dpqr-gompertz | mgompertz() |
Gen. Pareto | dpqr-gpd | mgpd() |
| Triangular | dpqr-tri | mtri() |
Moments for base R distributions
For these, d-p-q-r already exist in
stats – lumen only adds the moments function.
| Distribution | d-p-q-r | Moments |
| Beta | Beta | mbeta() |
| Binomial | Binomial | mbinom() |
| Chi-squared | Chisquare | mchisq() |
| Exponential | Exponential | mexp() |
| F | FDist | mf() |
| Gamma | GammaDist | mgamma() |
| Geometric | Geometric | mgeom() |
| Hypergeometric | Hypergeometric | mhyper() |
| Log-normal | Lognormal | mlnorm() |
Negative binomial | NegBinomial | mnbinom() |
| Normal | Normal | mnorm() |
| Poisson | Poisson | mpois() |
| Student's t | TDist | mt() |
Standalone
rsum1() generates a Dirichlet-distributed sample (which sums to 1
by construction), related to but not part of the
ddirichlet()/pdirichlet()/qdirichlet()/rdirichlet()
suite above.
pAD()/qAD() are the CDF and quantile function of the Anderson-Darling
test statistic's null distribution – supporting functions for
andersonDarlingTest(), not a distribution family of their
own (no d/r counterparts).