QBAsyDist (version 0.1.2)

LogLikQBAD: Log-likelihood function for the quantile-based asymmetric family of distributions.

Description

Log-Likelihood function \(\ell_n(\mu,\phi,\alpha)=\ln[L_n(\mu,\phi,\alpha)]\) in the three parameter quantile-based asymmetric family of densities defined in Section 3.2 of Gijbels et al. (2019a).

Usage

LogLikQBAD(y, mu, phi, alpha, f)

Arguments

y

This is a vector of quantiles.

mu

This is the location parameter \(\mu\).

phi

This is the scale parameter \(\phi\).

alpha

This is the index parameter \(\alpha\).

f

This is the reference density function \(f\) which is a standard version of a unimodal and symmetric around 0 density.

Value

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

References

Gijbels, I., Karim, R. and Verhasselt, A. (2019a). On quantile-based asymmetric family of distributions: properties and inference. International Statistical Review, https://doi.org/10.1111/insr.12324.

Examples

# NOT RUN {
# 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)
LogLikQBAD(y,mu=0,phi=1,alpha=0.5,f=f_N)

# 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)
LogLikQBAD(y,mu=0,phi=1,alpha=0.5,f=f_La)
# }