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

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

# 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.