# 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

 1 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

  1 2 3 4 5 6 7 8 9 10 # 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.