# momentAND: Moments estimation for the quantile-based asymmetric normal... In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## Description

Mean, variance, skewness, kurtosis and moments about the location parameter (i.e., αth quantile) of the quantile-based asymmetric normal distribution introduced in Gijbels et al. (2019a) useful for quantile regression with location parameter equal to μ, scale parameter φ and index parameter α.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```meanAND(mu, phi, alpha) varAND(mu, phi, alpha) skewAND(alpha) kurtAND(alpha) momentAND(phi, alpha, r) ```

## Arguments

 `mu` This is the location parameter μ. `phi` This is the scale parameter φ. `alpha` This is the index parameter α. `r` This is a value which is used to calculate rth moment about μ.

## Value

`meanAND` provides the mean, `varAND` provides the variance, `skewAND` provides the skewness, `kurtAND` provides the kurtosis, and `momentAND` provides the rth moment about the location parameter μ 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

 ```1 2 3 4 5 6``` ```# 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) ```

QBAsyDist documentation built on Sept. 4, 2019, 1:05 a.m.