# ALaD: Quantile-based asymmetric Laplace distribution In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

Density, cumulative distribution function, quantile function and random sample generation for the quantile-based asymmetric Laplace distribution (ALaD) discussed in Yu and Zhang (2005) and Gijbels et al. (2019a).

## Usage

 ```1 2 3 4 5 6 7``` ```dALaD(y, mu, phi, alpha) pALaD(q, mu, phi, alpha) qALaD(beta, mu, phi, alpha) rALaD(n, mu, phi, alpha) ```

## 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. `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

`dALaD` provides the density, `pALaD` provides the cumulative distribution function, `qALaD` provides the quantile function, and `rALaD` generates a random sample from the quantile-based asymmetric Laplace distribution. The length of the result is determined by n for `rALaD`, 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.

Yu., K, and Zhang, J. (2005). A three-parameter asymmetric Laplace distribution and its extension. Communications in Statistics–Theory and Methods, 34(9-10), 1867–1879.

`dQBAD`, `pQBAD`, `qQBAD`, `rQBAD`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# Density rnum<-rnorm(100) dALaD(y=rnum,mu=0,phi=1,alpha=.5) # Distribution function pALaD(q=rnum,mu=0,phi=1,alpha=.5) # Quantile function beta<-c(0.25,0.5,0.75) qALaD(beta=beta,mu=0,phi=1,alpha=.5) # random sample generation rALaD(n=100,mu=0,phi=1,alpha=.5) ```