QBAsyDist (version 0.1.2)

mleGTEF: Maximum likelihood estimation (MLE) for the generalized tick-exponential family (GTEF) of distributions.

Description

The log-likelihood function \(\ell_n(\eta,\phi,\alpha,p)=\ln[L_n(\eta,\phi,\alpha,p)]\) and parameter estimation of \( \theta=(\eta,\phi,\alpha,p)\) 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) \(f_{\alpha}^g(y;\eta,\phi)\), default -Inf.

upper

This is the upper limit of the domain (support of the random variable) \(f_{\alpha}^g(y;\eta,\phi)\), default Inf.

Value

The maximum likelihood estimate of parameter \(\theta=(\eta,\phi,\alpha,p)\) 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

# NOT RUN {
# 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
# }