# ALoD: Quantile-based asymmetric logistic distribution In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

Density, cumulative distribution function, quantile function and random sample generation from the quantile-based asymmetric logistic distribution (ALoD) proposed in Gijbels et al. (2019a).

## Usage

 ```1 2 3 4 5 6 7``` ```dALoD(y, mu, phi, alpha) pALoD(q, mu, phi, alpha) qALoD(beta, mu, phi, alpha) rALoD(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

`dALoD` provides the density, `pALoD` provides the cumulative distribution function, `qALoD` provides the quantile function, and `rALoD` generates a random sample from the quantile-based asymmetric logistic distribution. The length of the result is determined by n for `rALoD`, 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 logistic distribution (ALoD) # Density rnum<-rnorm(100) dALoD(y=rnum,mu=0,phi=1,alpha=.5) # Distribution function pALoD(q=rnum,mu=0,phi=1,alpha=.5) # Quantile function beta<-c(0.25,0.5,0.75) qALoD(beta=beta,mu=0,phi=1,alpha=.5) # random sample generation rALoD(n=100,mu=0,phi=1,alpha=.5) ```