QBAsyDist (version 0.1.2)

LogLikATD: Log-likelihood function for the quantile-based asymmetric Student's-\(t\) distribution.

Description

The log-likelihood function \(\ell_n(\mu,\phi,\alpha,\nu)=\ln[L_n(\mu,\phi,\alpha,\nu)]\) and parameter estimation of \( \theta=(\mu,\phi,\alpha,\nu)\) in the quantile-based asymmetric Student's-\(t\) distribution by using the maximum likelihood estimation are discussed in Gijbels et al. (2019a).

Usage

LogLikATD(y, mu, phi, alpha, nu)

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 \(\alpha\).

nu

This is the degrees of freedom parameter \(\nu\), which must be positive.

Value

LogLikATD provides the value of the Log-likelihood function of the quantile-based asymmetric Student's-\(t\) distribution.

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
y<-rnorm(100)
LogLikATD(y,mu=0,phi=1,alpha=0.5,nu=10)

# }