SSN: Standard Skewed Normal Parameterized using Skewness.
In cSFM: Covariate-adjusted Skewed Functional Model (cSFM)

Description Usage Arguments Details Value See Also Examples

Calculate the density function, log density function, and derivatives of the standard skewed normal (SSN) distribution parameterized using skewness.

1 2	g(y, gamma, log = FALSE) D.lg(y, gamma)

`y`	function arigument, taking values in the real line
`gamma`	skewness parameter; should have the same dimension as `y`
`log`	logical; if TRUE, the log of `g(y, gamma)` is given

Calculate the pdf (probability density function) and derivatives of standard skewed normal when parameterized by skewness.

g(y, gamma) gives the pdf value at y and gamma as the skewness; g(y, gamma, log = TRUE) gives the log of the pdf value at y and gamma as the skewness; D.lg(y, gamma) gives the list of derivatives of the log pdf at y and gamma with the following components:

`D1`	1st derivative of `log.g(y,gamma)` wrt. `y`
`D2`	1st derivative of `log.g(y,gamma)` wrt. `gamma`
`D12`	2nd cross-partial derivative of `log.g(y,gamma)` wrt. `y` and `gamma`
`D11`	2nd derivative of `log.g(y,gamma)` wrt. `y`
`D22`	2nd derivative of `log.g(y,gamma)` wrt. `gamma`

D.SN, shape.dp, skewness.cp, D.gamma

# pdf of SSN
ret1 <- g(seq(-3, 3, length = 100), 0.9)  
# plot the pdf
plot(seq(-3, 3, length = 100), ret1, type = "l", 
     xlab = "x", ylab = "pdf", main = "Plot of Stardard Skewed Normal Density")
# derivatives of pdf 
ret2 <- D.lg(10, 0.5) 
# y and a are a vector
ret3 <- D.lg(rnorm(10), seq(0.1,0.5,length = 10))   
# y and a are matrices
ret4 <- D.lg(matrix(rnorm(10), 2, 5), matrix(seq(0.1,0.5,length = 10), 2, 5))