The cdfquantreg family consists of the currently available distributions that can be used to fit quantile regression models via the cdfquantreg() function.
cdfqrFamily(shape = "all")A list of distributions that are available in the current version of package.
To show all distributions or the set of distribution for a specific type of shape. Can be BM, TM,LL or FT for Bimodal, Trimodal, Logit-logistic or Finite-tailed shapes, respectively.
The cdfquantreg package includes a two-parameter family of distributions for
modeling random variables on the (0, 1) interval by applying the cumulative
distribution function (cdf) of one “parent” distribution to the
quantile function of another.
The naming of these distributions is “parent - child” or
“fd - sd”, where “fd” is the parent distribution, and “sd”
is the child distribution.
The distributions have four characteristic shapes: Logit-logistic, bimodal, trimodal, and finite-tailed.
Here is the list of currently available distributions.
Bimodal Shape Distributions
| Distribution | R input | Alternative Input | Shape |
| Burr VII-ArcSinh | fd = "burr7", sd = "arcsinh" | family = "burr7-arcsinh" | Bimodal |
| Burr VII-Cauchy | fd = "burr7", sd = "cauchy" | family = "burr7-cauchy" | Bimodal |
| Burr VII-T2 | fd = "burr7", sd = "t2" | family = "burr7-t2" | Bimodal |
| Burr VIII-ArcSinh | fd = "burr8", sd = "arcsinh" | family = "burr8-arcsinh" | Bimodal |
| Burr VIII-Cauchy | fd = "burr8", sd = "cauchy" | family = "burr8-cauchy" | Bimodal |
| Burr VIII-T2 | fd = "burr8", sd = "t2" | family = "burr8-t2" | Bimodal |
| Logit-ArcSinh | fd = "logit", sd = "arcsinh" | family = "logit-arcsinh" | Bimodal |
| Logit-Cauchy | fd = "logit", sd = "cauchy" | family = "logit-cauchy" | Bimodal |
| Logit-T2 | fd = "logit", sd = "t2" | family = "logit-t2" | Bimodal |
| T2-ArcSinh | fd = "t2", sd = "arcsinh" | family = "t2-arcsinh" | Bimodal |
| T2-Cauchy | fd = "t2", sd = "cauchy" | family = "t2-cauchy" | Bimodal |
Trimodal Shape Distributions
| Distribution | R input | Alternative Input | Shape |
| ArcSinh-Burr VII | fd = "arcsinh", sd = "burr7" | family = "arcsinh-burr7" | Trimodal |
| ArcSinh-Burr VIII | fd = "arcsinh", sd = "burr8" | family = "arcsinh-burr8" | Trimodal |
| ArcSinh-Logistic | fd = "arcsinh", sd = "logistic" | family = "arcsinh-logistic" | Trimodal |
| ArcSinh-T2 | fd = "arcsinh", sd = "t2" | family = "arcsinh-t2" | Trimodal |
| Cauchit-Burr VII | fd = "cauchit", sd = "burr7" | family = "cauchit-burr7" | Trimodal |
| Cauchit-Burr VIII | fd = "cauchit", sd = "burr8" | family = "cauchit-burr8" | Trimodal |
| Cauchit-Logistic | fd = "cauchit", sd = "logistic" | family = "cauchit-logistic" | Trimodal |
| Cauchit-T2 | fd = "cauchit", sd = "t2" | family = "cauchit-t2" | Trimodal |
| T2-Burr VII | fd = "t2", sd = "burr7" | family = "t2-burr7" | Trimodal |
| T2-Burr VIII | fd = "t2", sd = "burr8" | family = "t2-burr8" | Trimodal |
| T2-Logistic | fd = "t2", sd = "logistic" | family = "t2-logistic" | Trimodal |
Logit-logistic Shape Distributions
| Distribution | R input | Alternative Input | Shape |
| Burr VII-Burr VII | fd = "burr7", sd = "burr7" | family = "burr7-burr7" | Logit-logistic |
| Burr VII-Burr VIII | fd = "burr7", sd = "burr8" | family = "burr7-burr8" | Logit-logistic |
| Burr VII-Logistic | fd = "burr7", sd = "logistic" | family = "burr7-logistic" | Logit-logistic |
| Burr VIII-Burr VII | fd = "burr8", sd = "burr7" | family = "burr8-burr7" | Logit-logistic |
| Burr VIII-Burr VIII | fd = "burr8", sd = "burr8" | family = "burr8-burr8" | Logit-logistic |
| Burr VIII-Logistic | fd = "burr8", sd = "logistic" | family = "burr8-logistic" | Bimodal |
| Logit-Burr VII | fd = "logit", sd = "burr7" | family = "logit-burr7" | Logit-logistic |
| Logit-Burr VIII | fd = "logit", sd = "burr8" | family = "logit-burr8" | Logit-logistic |
| Logit-Logistic | fd = "logit", sd = "logistic" | family = "logit-logistic" | Logit-logistic |
Finite-tailed Shape Distributions
| Distribution | R input | Alternative Input | Shape |
| ArcSinh-ArcSinh | fd = "arcsinh", sd = "arcsinh" | family = "arcsinh-arcsinh" | Finite-tailed |
| ArcSinh-Cauchy | fd = "arcsinh", sd = "cauchy" | family = "arcsinh-cauchy" | Finite-tailed |
| Cauchit-ArcSinh | fd = "cauchit", sd = "arcsinh" | family = "cauchit-arcsinh" | Finite-tailed |
| Cauchit-Cauchy | fd = "cauchit", sd = "cauchy" | family = "cauchit-cauchy" | Finite-tailed |
| T2-T2 | fd = "t2", sd = "t2" | family = "t2-t2" | Finite-tailed |
Kumaraswamy Distribution
| Distribution | R input | Alternative Input | Shape |
| Kumaraswamy | fd = "", sd = "" | family = "-" |