QBAsyDist (version 0.1.2)

mleAND: Maximum likelihood estimation (MLE) for the quantile-based asymmetric normal distribution.

Description

The log-likelihood function \(\ell_n(\mu,\phi,\alpha)=\ln[L_n(\mu,\phi,\alpha)]\) and parameter estimation of \( \theta=(\mu,\phi,\alpha)\) in the asymmetric normal distribution by using the maximum likelihood estimation are discussed in Gijbels et al. (2019a).

Usage

mleAND(y, alpha = NULL)

Arguments

y

This is a vector of quantiles.

alpha

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

Value

The maximum likelihood estimate of parameter \(\theta=(\mu,\phi,\alpha)\) of the quantile-based asymmetric normal 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 {
# Maximum likelihood estimation
y=rnorm(100)
mleAND(y)
mleAND(y,alpha=0.5)
# }