# mleGAD: Maximum likelihood estimation (MLE) for the generalized... In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

The log-likelihood function \ell_n(η,φ,α)=\ln[L_n(η,φ,α)] and parameter estimation of θ=(η,φ,α) in the three parameter generalized quantile-based asymmetric family of densities by using the maximum likelihood estimation are discussed in Gijbels et al. (2019b).

## Usage

 1 mleGAD(y, f, g, lower = -Inf, upper = Inf) 

## 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. g This is the "link" function. The function g is to be differentiated. Therefore, g must be written as a function. For example, g<-function(y){log(y)} for log link function. lower This is the lower limit of the domain (support of the random variable) f_{α}^g(y;η,φ), default -Inf. upper This is the upper limit of the domain (support of the random variable) f_{α}^g(y;η,φ), default Inf.

## Value

The maximum likelihood estimate of parameter θ=(η,φ,α) of the generalized quantile-based asymmetric family of densities

## References

Gijbels, I., Karim, R. and Verhasselt, A. (2019b). Quantile estimation in a generalized asymmetric distributional setting. To appear in Springer Proceedings in Mathematics & Statistics, Proceedings of ‘SMSA 2019’, the 14th Workshop on Stochastic Models, Statistics and their Application, Dresden, Germany, in March 6–8, 2019. Editors: Ansgar Steland, Ewaryst Rafajlowicz, Ostap Okhrin.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 # 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) y<-rnorm(100) g_id<-function(y){y} g_log<-function(y){log(y)} mleGAD(y,f=f_N,g=g_id) # For identity-link mleGAD(rexp(100,0.1),f=f_N,g=g_log,lower = 0, upper = Inf) # For log-link # 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) mleGAD(y,f=f_La,g=g_id) # For identity-link mleGAD(rexp(100,0.1),f=f_La,g=g_log,lower = 0, upper = Inf) # For log-link 

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