cdfqrFamily: Overview of the family of distributions
In cdfquantreg: Quantile Regression for Random Variables on the Unit Interval

cdfqrFamily

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