splitn_moments function

Moments of the split normal distribution

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

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.

Returns

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.

Examples

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)

References

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

See Also

psplitn() dsplitn() qsplitn() and rsplitn() for the split-normal distribution.

Author(s)

Feng Li, Jiayue Zeng