mleQBAD: Maximum likelihood estimation (MLE) for the quantile-based...

In QBAsyDist: Asymmetric Distributions and Quantile Estimation

Description

The log-likelihood function \ell_n(μ,φ,α)=\ln[L_n(μ,φ,α)] and parameter estimation of θ=(μ,φ,α) 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 α.

Value

The maximum likehood estimate of paramter θ=(μ,φ,α) 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

# 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)

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