splitt_kurtosis {dng} R Documentation

## Moments of the split-t distribution

### Description

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

### Usage

```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)

### Value

`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.

### Author(s)

Feng Li, Jiayue Zeng

### 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.

`dsplitt()`, `psplitt()`, `qsplitt()` and `rsplitt()` 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)
```

[Package dng version 0.2.1 Index]