QBAsyDist (version 0.1.2)

momentALoD: Moments estimation for the quantile-based asymmetric logistic distribution.

Description

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

Usage

meanALoD(mu, phi, alpha)
varALoD(mu, phi, alpha)
skewALoD(alpha)
kurtALoD(alpha)
momentALoD(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 the \(r\)th moment about \(\mu\).

Value

meanALoD provides the mean, varALoD provides the variance, skewALoD provides the skewness, kurtALoD provides the kurtosis, and momentALoD provides the \(r\)th moment about the location parameter \(\mu\) of the quantile-based asymmetric logistic 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
meanALoD(mu=0,phi=1,alpha=0.5)
varALoD(mu=0,phi=1,alpha=0.5)
skewALoD(alpha=0.5)
kurtALoD(alpha=0.5)
momentALoD(phi=1,alpha=0.5,r=1)


# }