mleALD {ald} | R Documentation |
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
.
mleALD(y, initial = NA)
y |
observation vector. |
initial |
optional vector of initial values c(μ,σ,p). |
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.
The function returns a list with two objects
iter |
iterations to reach convergence. |
par |
vector of Maximum Likelihood Estimators. |
Christian E. Galarza <cgalarza88@gmail.com> and Victor H. Lachos <hlachos@ime.unicamp.br>
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.
## 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")