# splitn_moments: Moments of the split normal distribution In dng: Distributions and Gradients

## Description

Computing the mean, variance, skewness and kurtosis for the split-normal distribution.

## Usage

 ```1 2 3 4 5 6 7``` ```splitn_kurtosis(lmd) splitn_mean(mu, sigma, lmd) splitn_skewness(sigma, lmd) splitn_var(sigma, lmd) ```

## Arguments

 `lmd` vector of skewness parameters (>0). If is 1, reduce to normal distribution. `mu` vector of location parameter. (The mode of the density) `sigma` vector of standard deviations.

## Value

`splitn_mean` gives the mean. `splitn_var` gives the variance. `splitn_skewness` gives the skewness. `splitn_kurtosis` gives the kurtosis. (`splitn_mean`, `splitn_var`,`splitn_skeness` and `splitn_kurtosis` are all vectors.

## Functions

• `splitn_kurtosis`: Kurtosis for the split-normal distribution.

• `splitn_skewness`: Skewness for the split-normal distribution.

• `splitn_var`: Variance for the split-normal distribution.

## Author(s)

Feng Li, Jiayue Zeng

## References

Villani, M., & Larsson, R. (2006) The Multivariate Split Normal Distribution and Asymmetric Principal Components Analysis. Sveriges Riksbank Working Paper Series, No. 175.

`psplitn()` `dsplitn()` `qsplitn()` and `rsplitn()` for the split-normal distribution.
 ```1 2 3 4 5 6 7 8``` ```mu <- c(0,1,2) sigma <- c(0.5,1,2) lmd <- c(1,2,3) mean0 <- splitn_mean(mu, sigma, lmd) var0 <- splitn_var(sigma, lmd) skewness0 <- splitn_skewness(sigma, lmd) kurtosis0 <- splitn_kurtosis(lmd) ```