dCN {ContaminatedMixt}

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.

See Also

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)