QBAsyDist (version 0.1.2)

LogLikAEPD: Log-likelihood function for the quantile-based asymmetric exponential power distribution (AEPD) of distributions.

Description

Log-Likelihood function \(\ell_n(\mu,\phi,\alpha,p)=\ln[L_n(\mu,\phi,\alpha,p)]\) in the quantile-based asymmetric exponential power distribution (AEPD) of densities defined in Gijbels et al. (2019b).

Usage

LogLikAEPD(y, mu, phi, alpha, p)

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 \(\alpha\).

p

This is the shape parameter, which must be positive.

Value

LogLikAEPD provides the realized value of the Log-likelihood function 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
y<-rnorm(100)
LogLikAEPD(rexp(100,0.1),mu=10,phi=1,alpha=0.5,p=2)


# }