# pcsn: The cumulative distribution function In csn: Closed Skew-Normal Distribution

## Description

The cumulative distribution function of the closed-skew normal distribution

## Usage

 `1` ```pcsn(x, mu, sigma, gamma, nu, delta) ```

## Arguments

 `x` this is either a vector of length `n` or a matrix with `n` columns, where `n=ncol(sigma)`, giving the coordinates of the point(s) where the cdf must be evaluated `mu` a numeric vector representing the location parameter of the distribution; it must be of length `n`, as defined above `sigma` a positive definite matrix representing the scale parameter of the distribution; a vector of length 1 is also allowed `gamma` a matrix representing the skewness parameter of the distribution; a vector of length 1 is also allowed `nu` a numeric vector allows for closure with conditional densities; it must be of length `q`, as defined above `delta` a positive definite matrix allows for closure with the marginal densities; a vector of length 1 is also allowed

## Details

Function pcsn makes use of pmvnorm from package mvtnorm

## Value

`pcsn` returns a vector of cdf values

`pmvnorm`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```x1 <- seq(4,6,by = 0.1) x2 <- x1+sin(x1) x3 <- x1-cos(x1) x <- cbind(x1,x2,x3) mu <- c(1,2,3) sigma <- matrix(c(2,-1,0,-1,2,-1,0,-1,2),3) gamma <- matrix(c(0,1,0,2,2,3),2,3) nu <- c(1,3) delta <- matrix(c(1,1,1,2),2) pcsn(6,5,9,1,0,0.05) pcsn(c(3,4,5),mu,sigma,gamma,nu,delta) pcsn(x,mu,sigma,gamma,nu,delta) ```