mleALD {ald}R Documentation

Maximum Likelihood Estimators (MLE) for the Asymmetric Laplace Distribution

Description

Maximum Likelihood Estimators (MLE) for the Three-Parameter Asymmetric Laplace Distribution defined in Koenker and Machado (1999) useful for quantile regression with location parameter equal to mu, scale parameter sigma and skewness parameter p.

Usage

mleALD(y, initial = NA)

Arguments

y

observation vector.

initial

optional vector of initial values c(μ,σ,p).

Details

The algorithm computes iteratevely the MLE's via the combination of the MLE expressions for μ and σ, and then maximizing with rescpect to p the Log-likelihood function (likALD) using the well known optimize R function. By default the tolerance is 10^-5 for all parameters.

Value

The function returns a list with two objects

iter

iterations to reach convergence.

par

vector of Maximum Likelihood Estimators.

Author(s)

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

References

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.

See Also

ALD,momentsALD,likALD

Examples

## Let's try this function

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")


[Package ald version 1.3.1 Index]