# ald-package: The Asymmetric Laplace Distribution In ald: The Asymmetric Laplace Distribution

## Description

It provides the density, distribution function, quantile function, random number generator, likelihood function, moments and Maximum Likelihood estimators for a given sample, all this for the three parameter Asymmetric Laplace Distribution defined in Koenker and Machado (1999) useful for quantile regression.

## Details

 Package: ald Type: Package Version: 1.0 Date: 2015-01-27 License: GPL (>=2)

## Author(s)

Christian E. Galarza <cgalarza88@gmail.com> and Victor H. Lachos <hlachos@ime.unicamp.br>

## References

Koenker, R., Machado, J. (1999). Goodness of fit and related inference processes for quantile regression. J. Amer. Statist. Assoc. 94(3):1296-1309.

Yu, K. & Moyeed, R. (2001). Bayesian quantile regression. Statistics & Probability Letters, 54(4), 437-447.

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

`ALD`,`momentsALD`,`likALD`,`mleALD`

## 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``` ```## Let's plot an Asymmetric Laplace Distribution! ##Density sseq = seq(-40,80,0.5) dens = dALD(y=sseq,mu=50,sigma=3,p=0.75) plot(sseq,dens,type="l",lwd=2,col="red",xlab="x",ylab="f(x)", main="ALD Density function") ## Distribution Function df = pALD(q=sseq,mu=50,sigma=3,p=0.75) plot(sseq,df,type="l",lwd=2,col="blue",xlab="x",ylab="F(x)", main="ALD Distribution function") abline(h=1,lty=2) ##Inverse Distribution Function prob = seq(0,1,length.out = 1000) idf = qALD(prob=prob,mu=50,sigma=3,p=0.75) plot(prob,idf,type="l",lwd=2,col="gray30",xlab="x",ylab=expression(F^{-1}~(x))) title(main="ALD Inverse Distribution function") abline(v=c(0,1),lty=2) #Random Sample Histogram sample = rALD(n=10000,mu=50,sigma=3,p=0.75) hist(sample,breaks = 70,freq = FALSE,ylim=c(0,max(dens)),main="") title(main="Histogram and True density") lines(sseq,dens,col="red",lwd=2) ## Let's compute the MLE's param = c(-323,40,0.9) y = rALD(10000,mu = param[1],sigma = param[2],p = param[3]) #A random sample res = mleALD(y) #Comparing cbind(param,res\$par) #Let's plot seqq = seq(min(y),max(y),length.out = 1000) dens = dALD(y=seqq,mu=res\$par[1],sigma=res\$par[2],p=res\$par[3]) hist(y,breaks=50,freq = FALSE,ylim=c(0,max(dens))) lines(seqq,dens,type="l",lwd=2,col="red",xlab="x",ylab="f(x)", main="ALD Density function") ```

ald documentation built on April 5, 2021, 1:06 a.m.