dCN {ContaminatedMixt} R Documentation

## Multivariate Contaminated Normal Distribution

### Description

Probability density function and random number generation for the multivariate contaminated normal distribution.

### Usage

```dCN(x, mu = rep(0,p), Sigma, alpha = 0.99, eta = 1.01)
rCN(n, mu = rep(0,p), Sigma, alpha = 0.99, eta = 1.01)
```

### Arguments

 `x` either a vector of length `p` or a matrix with `p` columns, being `p = ncol(Sigma)`, representing the coordinates of the point(s) where the density must be evaluated `mu` either a vector of length `p`, representing the mean value, or (except for `rCN`) a matrix whose rows represent different mean vectors; if it is a matrix, its dimensions must match those of `x` `Sigma` a symmetric positive-definite matrix representing the scale matrix of the distribution; a vector of length 1 is also allowed (in this case, `p = 1` is set) `alpha` proportion of good observations; it must be a number between 0 and 1 `eta` degree of contamination; it should be a number greater than 1 `n` the number of random vectors to be generated

### Value

`dCN` returns a vector of density values; `rCN` returns a matrix of `n` rows of random vectors

### Author(s)

Antonio Punzo, Angelo Mazza, Paul D. McNicholas

### References

Punzo A., Mazza A. and McNicholas P. D. (2018). ContaminatedMixt: An R Package for Fitting Parsimonious Mixtures of Multivariate Contaminated Normal Distributions. Journal of Statistical Software, 85(10), 1–25.

Punzo A. and McNicholas P. D. (2016). Parsimonious mixtures of multivariate contaminated normal distributions. Biometrical Journal, 58(6), 1506–1537.

`ContaminatedMixt-package`

### Examples

```
point <- c(0,0,0)
mu <- c(1,-2,3)
Sigma <- diag(3)
alpha <- 0.8
eta <- 5
f <- dCN(point, mu, Sigma, alpha, eta)
x <- rCN(10, mu, Sigma, alpha, eta)

```

[Package ContaminatedMixt version 1.3.6 Index]