QBAsyDist (version 0.1.2)

mleAEPD: Maximum likelihood estimation (MLE) for the quantile-based asymmetric exponential power distribution.

Description

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

Usage

mleAEPD(y)

Arguments

y

This is a vector of quantiles.

Value

The maximum likelihood estimate of parameter \(\theta=(\mu,\phi,\alpha,p)\) of the quantile-based asymmetric exponential power distribution.

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

# NOT RUN {
# Example
rnum=rnorm(100)
mleAEPD(rnum)
# }