# The cumulative distribution function

### Description

The cumulative distribution function of the closed-skew normal distribution

### Usage

1 |

### Arguments

`x` |
this is either a vector of length |

`mu` |
a numeric vector representing the location parameter of the
distribution; it must be of length |

`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 |

`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

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)
``` |

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