QBAsyDist (version 0.1.2)

mleATD: Maximum likelihood estimation (MLE) 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

mleATD(y)

Arguments

y

This is a vector of quantiles.

Value

The maximum likelihood estimate of parameter \(\theta=(\mu,\phi,\alpha,\nu)\) 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(20)
mleATD(y)

# }