# ATD: Quantile-based asymmetric Student's-t distribution In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

Density, cumulative distribution function, quantile function and random sample generation from the quantile-based asymmetric Student's-t distribution (ATD) proposed in Gijbels et al. (2019a).

## Usage

 ```1 2 3 4 5 6 7``` ```dATD(y, mu, phi, alpha, nu) pATD(q, mu, phi, alpha, nu) qATD(beta, mu, phi, alpha, nu) rATD(n, mu, phi, alpha, nu) ```

## Arguments

 `y, q` These are each a vector of quantiles. `mu` This is the location parameter μ. `phi` This is the scale parameter φ. `alpha` This is the index parameter α. `nu` This is the degrees of freedom parameter ν, which must be positive. `beta` This is a vector of probabilities. `n` This is the number of observations, which must be a positive integer that has length 1.

## Value

`dATD` provides the density, `pATD` provides the cumulative distribution function, `qATD` provides the quantile function, and `rATD` generates a random sample from the quantile-based asymmetric Student's-t distribution. The length of the result is determined by n for `rATD`, and is the maximum of the lengths of the numerical arguments for the other functions.

## References

Gijbels, I., Karim, R. and Verhasselt, A. (2019a). On quantile-based asymmetric family of distributions: properties and inference. International Statistical Review, https://doi.org/10.1111/insr.12324.

`dQBAD`, `pQBAD`, `qQBAD`, `rQBAD`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```# Quantile-based asymmetric Student's-\eqn{t} distribution (ATD) # Density rnum<-rnorm(100) dATD(rnum,mu=0,phi=1,alpha=0.5,nu=10) # Distribution function pATD(rnum,mu=0,phi=1,alpha=0.5,nu=10) # Quantile function beta<-c(0.25,0.5,0.75) qATD(beta=beta,mu=0,phi=1,alpha=.5,nu=10) # random sample generation rATD(n=100,mu=0,phi=1,alpha=.5,nu=10) ```