# LogLikGAD: Log-likelihood function for the generalized quantile-based... In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

Log-Likelihood function \ell_n(η,φ,α)=\ln[L_n(η,φ,α)] in the three parameter generalized quantile-based asymmetric family of densities defined in Gijbels et al. (2019b).

## Usage

 1 LogLikGAD(y, eta, phi, alpha, f, g) 

## Arguments

 y This is a vector of quantiles. eta This is the location parameter η. phi This is the scale parameter φ. alpha This is the index parameter α. 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.

## Value

LogLikGAD provides the realized value of the Log-likelihood function of the generalized quantile-based asymmetric family of distributions.

## 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)} LogLikGAD(y,eta=0,phi=1,alpha=0.5,f=f_N,g=g_id) # For identity-link LogLikGAD(rexp(100,0.1),eta=10,phi=1,alpha=0.5,f=f_N,g=g_log) # 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) LogLikGAD(y,eta=0,phi=1,alpha=0.5,f=f_La,g=g_id) # For identity-link LogLikGAD(rexp(100,0.1),eta=10,phi=1,alpha=0.5,f=f_La,g=g_log) # For log-link 

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