# QBAD: Quantile-based asymmetric family of distributions In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

Density, cumulative distribution function, quantile function and random sample generation from the quantile-based asymmetric family of densities defined in Gijbels et al. (2019a).

## Usage

 ```1 2 3 4 5 6 7``` ```dQBAD(y, mu, phi, alpha, f) pQBAD(q, mu, phi, alpha, F) qQBAD(beta, mu, phi, alpha, F, QF = NULL) rQBAD(n, mu, phi, alpha, F, QF = NULL) ```

## 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. `f` This is the reference density function f which is a standard version of a unimodal and symmetric around 0 density. `F` This is the cumulative distribution function F of a unimodal and symmetric around 0 reference density function f. `beta` This is a vector of probabilities. `QF` This is the quantile function of the reference density f. `n` This is the number of observations, which must be a positive integer that has length 1.

## Value

`dQBAD` provides the density, `pQBAD` provides the cumulative distribution function, `qQBAD` provides the quantile function, and `rQBAD` generates a random sample from the quantile-based asymmetric family of distributions. The length of the result is determined by n for `rQBAD`, 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.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```# Example 1: Let F be a standard normal cumulative distribution function then f_N<-function(s){dnorm(s, mean = 0,sd = 1)} # density function of N(0,1) F_N<-function(s){pnorm(s, mean = 0,sd = 1)} # distribution function of N(0,1) QF_N<-function(beta){qnorm(beta, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)} rnum<-rnorm(100) beta=c(0.25,0.50,0.75) # Density dQBAD(y=rnum,mu=0,phi=1,alpha=.5,f=f_N) # Distribution function pQBAD(q=rnum,mu=0,phi=1,alpha=.5,F=F_N) # Quantile function qQBAD(beta=beta,mu=0,phi=1,alpha=.5,F=F_N,QF=QF_N) qQBAD(beta=beta,mu=0,phi=1,alpha=.5,F=F_N) # random sample generation rQBAD(n=100,mu=0,phi=1,alpha=.5,QF=QF_N) rQBAD(n=100,mu=0,phi=1,alpha=.5,F=F_N) # Example 2: Let F be a standard Laplace cumulative distribution function then f_La<-function(s){0.5*exp(-abs(s))} # density function of Laplace(0,1) F_La<-function(s){0.5+0.5*sign(s)*(1-exp(-abs(s)))} # distribution function of Laplace(0,1) QF_La<-function(beta){-sign(beta-0.5)*log(1-2*abs(beta-0.5))} rnum<-rnorm(100) beta=c(0.25,0.50,0.75) # Density dQBAD(y=rnum,mu=0,phi=1,alpha=.5,f=f_La) # Distribution function pQBAD(q=rnum,mu=0,phi=1,alpha=.5,F=F_La) # Quantile function qQBAD(beta=c(0.25,0.50,0.75),mu=0,phi=1,alpha=.5,F=F_La,QF=QF_La) qQBAD(beta=c(0.25,0.50,0.75),mu=0,phi=1,alpha=.5,F=F_La) # random sample generation rQBAD(n=100,mu=0,phi=1,alpha=.5,QF=QF_La) rQBAD(n=100,mu=0,phi=1,alpha=.5,F=F_La) ```

QBAsyDist documentation built on Sept. 4, 2019, 1:05 a.m.