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

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

# 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.