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]