QBAsyDist (version 0.1.2)

momentALaD: Moments estimation for the quantile-based asymmetric Laplace distribution.

Description

Mean, variance, skewness, kurtosis and moments about the location parameter (i.e., \(\alpha\)th quantile) of the quantile-based asymmetric Laplace distribution studied in Gijbels et al. (2019a) useful for quantile regression with location parameter equal to \(\mu\), scale parameter \(\phi\) and index parameter \(\alpha\).

Usage

meanALaD(mu, phi, alpha)
varALaD(mu, phi, alpha)
skewALaD(alpha)
kurtALaD(alpha)
momentALaD(phi, alpha, r)

Arguments

mu

This is the location parameter \(\mu\).

phi

This is the scale parameter \(\phi\).

alpha

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

r

This is a value which is used to calculate \(r\)th moment about \(\mu\).

Value

meanALaD provides the mean, varALaD provides the variance, skewALaD provides the skewness, kurtALaD provides the kurtosis, and momentALaD provides the \(r\)th moment about the location parameter \(\mu\) of the quantile-based asymmetric Laplace 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
meanALaD(mu=0,phi=1,alpha=0.5)
varALaD(mu=0,phi=1,alpha=0.5)
skewALaD(alpha=0.5)
kurtALaD(alpha=0.5)
momentALaD(phi=1,alpha=0.5,r=1)
# }