The cumulative distribution function

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Description

The cumulative distribution function of the closed-skew normal distribution

Usage

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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

See Also

pmvnorm

Examples

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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)

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