QBAsyDist (version 0.1.2)

mleQBAD: Maximum likelihood estimation (MLE) for the quantile-based asymmetric family of distributions.

Description

The log-likelihood function \(\ell_n(\mu,\phi,\alpha)=\ln[L_n(\mu,\phi,\alpha)]\) and parameter estimation of \( \theta=(\mu,\phi,\alpha)\) in the three parameter quantile-based asymmetric family of densities by using the maximum likelihood estimation are discussed in Section 3.2 of Gijbels et al. (2019a).

Usage

mleQBAD(y, f, alpha = NULL)

Arguments

y

This is a vector of quantiles.

f

This is the reference density function \(f\) which is a standard version of a unimodal and symmetric around 0 density.

alpha

This is the index parameter \(\alpha\).

Value

The maximum likehood estimate of paramter \(\theta=(\mu,\phi,\alpha)\) of the quantile-based asymmetric family of densities

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

# NOT RUN {
# 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)
rnum=rnorm(100)
mleQBAD(rnum,f=f_N)
mleQBAD(rnum,f=f_N,alpha=.5)

# 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)
mleQBAD(rnum,f=f_La)
mleQBAD(rnum,f=f_La,alpha=.5)
# }