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QBAsyDist (version 0.1.2)

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.

Examples

Run this code
# NOT RUN {
# Example
meanAND(mu=0,phi=1,alpha=0.5)
varAND(mu=0,phi=1,alpha=0.5)
skewAND(alpha=0.5)
kurtAND(alpha=0.5)
momentAND(phi=1,alpha=0.5,r=1)


# }

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