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

## Description

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

## Usage

 1 mleGTEF(y, g, lower = -Inf, upper = Inf) 

## Arguments

 y This is a vector of quantiles. 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,p) of the generalized tick-exponential 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 # Example rnum=rnorm(100) g_id<-function(y){y} g_log<-function(y){log(y)} mleGTEF(rnum,g_id) # For identity-link mleGTEF(rexp(100),g_log,lower = 0, upper = Inf) # For log-link 

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