cdfqrFamily {cdfquantreg}R Documentation

Overview of the family of distributions

Description

The cdfquantreg family consists of the currently available distributions that can be used to fit quantile regression models via the cdfquantreg() function.

Usage

cdfqrFamily(shape = "all")

Arguments

shape

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.

Details

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 = "-"

Value

A list of distributions that are available in the current version of package.

Examples

cdfqrFamily()


[Package cdfquantreg version 1.2.5 Index]