splitn {dng} R Documentation

## Split-normal distribution

### Description

Density distribution function, quantile function and random generation function for the split normal distribution.

### Usage

dsplitn(x, mu, sigma, lmd, logarithm)

psplitn(q, mu, sigma, lmd)

qsplitn(p, mu, sigma, lmd)

rsplitn(n, mu, sigma, lmd)


### Arguments

 x vector of quantiles. mu vector of location parameter. (The mode of the density) sigma vector of standard deviations. lmd vector of skewness parameters (>0). If is 1, reduced to symmetric normal distribution. logarithm logical; if TRUE, probabilities p are given as log(p). q vector of quantiles. p vector of probability. n number of observations. If length(n) > 1, the length is taken to be the number required.

### Details

The random ' variable y follows a split-normal distribution, y~N(\mu, ' \sigma, \lambda), which has density:

1/(1+\lambda)\sigma ' \sqrt(2/\pi) exp{-(y-\mu)*2/2\sigma^2}, if y<=\mu

'

1/(1+\lambda)\sigma \sqrt(2/\pi) exp{-(y-\mu)*2/2\sigma^2 \lambda^2}, ' if y>\mu

where \sigma>0 and \lambda>0. The Split-normal ' distribution reduce to normal distribution when \lambda=1.

### Value

dsplitn gives the density; psplitn gives the percentile; qsplitn gives the quantile; and rsplitn gives the random variables. Invalid arguments will result in return value NaN, with a warning.

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

### Functions

• psplitn: Percentile for the split-normal distribution.

• qsplitn: Quantile for the split-normal distribution.

• rsplitn: Randon variables from 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.

splitn_mean(), splitn_var(),splitn_skewness() and splitn_kurtosis() for numerical characteristics of the split-normal distribution.

### Examples


n <- 3
mu <- c(0,1,2)
sigma <- c(1,2,3)
lmd <- c(1,2,3)

q0 <- rsplitn(n, mu, sigma, lmd)
d0 <- dsplitn(q0, mu, sigma, lmd, logarithm = FALSE)
p0 <- psplitn(q0, mu, sigma, lmd)
q1 <- qsplitn(p0,mu, sigma, lmd)
all.equal(q0, q1)


[Package dng version 0.2.1 Index]