momentAND: Moments estimation for the quantile-based asymmetric normal distribution.
Description
Mean, variance, skewness, kurtosis and moments about the location parameter (i.e., \(\alpha\)th quantile) of the quantile-based asymmetric normal distribution introduced in Gijbels et al. (2019a) useful for quantile regression with location parameter equal to \(\mu\), scale parameter \(\phi\) and index parameter \(\alpha\).
Usage
meanAND(mu, phi, alpha)
varAND(mu, phi, alpha)
skewAND(alpha)
kurtAND(alpha)
momentAND(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
meanAND provides the mean, varAND provides the variance, skewAND provides the skewness, kurtAND provides the kurtosis, and momentAND provides the \(r\)th moment about the location parameter \(\mu\) 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.