QBAsyDist (version 0.1.2)

momentATD: Moments estimation for the quantile-based asymmetric Student's-\(t\) distribution.

Description

Mean, variance, skewness, kurtosis and moments about the location parameter (i.e., \(\alpha\)th quantile) of the quantile-based asymmetric Student's-\(t\) 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

meanATD(mu, phi, alpha, nu)
varATD(mu, phi, alpha, nu)
skewATD(alpha, nu)
kurtATD(alpha, nu)
momentATD(phi, alpha, nu, r)

Arguments

mu

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

phi

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

alpha

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

nu

This is the degrees of freedom parameter \(\nu\), which must be positive.

r

This is a value which is used to calculate the \(r\)th moment \((r\in\{1,2,3,4\})\) about \(\mu\).

Value

meanATD provides the mean, varATD provides the variance, skewATD provides the skewness, kurtATD provides the kurtosis, and momentATD provides the \(r\)th moment about the location parameter \(\mu\) of the quantile-based asymmetric Student's-\(t\) 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
meanATD(mu=0,phi=1,alpha=0.5,nu=10)
varATD(mu=0,phi=1,alpha=0.5,nu=10)
skewATD(alpha=0.5,nu=10)
kurtATD(alpha=0.5,nu=10)
momentATD(phi=1,alpha=0.5,nu=10,r=1)


# }