splitt_moments function

Moments of the split-t distribution

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

splitt_kurtosis(df, phi, lmd)

splitt_mean(mu, df, phi, lmd)

splitt_skewness(df, phi, lmd)

splitt_var(df, phi, lmd)

Arguments

• df: degrees of freedom (> 0, can be non-integer). df = Inf is allowed.
• phi: vector of scale parameters (> 0).
• lmd: vector of skewness parameters (> 0). If is 1, reduced to symmetric student t distribution.
• mu: vector of location parameter. (The mode of the density)

Returns

splitt_mean gives the mean. splitt_var gives the variance. splitt_skewness gives the skewness. splitt_kurtosis

gives the kurtosis. (splitt_mean, splitt_var,splitt_skeness and splitt_kurtosis are all vectors.)

Invalid arguments will result in return value NaN, with a warning.

Functions

• splitt_kurtosis: Kurtosis for the split-t distribution.
• splitt_skewness: Skewness for the split-t distribution.
• splitt_var: Variance for the split-t distribution.

Examples

mu <- c(0,1,2)
df <- rep(10,3)
phi <- c(0.5,1,2)
lmd <- c(1,2,3)

mean0 <- splitt_mean(mu, df, phi, lmd)
var0 <- splitt_var(df, phi, lmd)
skewness0 <- splitt_skewness(df, phi, lmd)
kurtosis0 <- splitt_kurtosis(df, phi, lmd)

References

Li, F., Villani, M., & Kohn, R. (2010). Flexible modeling of conditional distributions using smooth mixtures of asymmetric student t densities. Journal of Statistical Planning & Inference, 140(12), 3638-3654.

See Also

dsplitt(), psplitt(), qsplitt() and rsplitt() for the split-t distribution.

Author(s)

Feng Li, Jiayue Zeng