rmscn {MSclust}

Multiple Scaled Contaminated Normal Distribution

Description

Probability density function and pseudo random number generation for the multiple scaled contaminated normal distribution.

Usage

  dmscn(x,  mu = NULL, L = NULL, G = NULL, Sigma = NULL, alpha = NULL, eta = NULL)
rmscn(n,d=2,mu=rep(0,d),L=NULL,G=NULL,Sigma=diag(d),alpha=rep(0.99,d),eta=rep(1.01,d))

Arguments

x

A matrix or data frame such that rows correspond to observations and columns correspond to variables.

n

The number of random vectors to be generated.

d

A number specifing the dimenstion.

mu

Either a vector of length d, representing the mean value, or (except for rmscn) a matrix whose rows represent different mean vectors; if it is a matrix, its dimensions must match those of x.

L

Lambda diagonal d-dimensional matrix of the eigenvalues of Sigma.

G

Gamma orthogonal d-dimensional matrix whose columns are the normalized eigenvectors of Sigma.

Sigma

A symmetric positive-definite d-dimensional matrix representing the scale matrix of the distribution; a vector of length 1 is also allowed (in this case, d = 1 is set). Identity matrix by default.

alpha

d-dimensional vector containing the proportion of good observations; it must be a number between 0 and 1.

eta

d-dimensional vector containing the degree of contamination; it should be a number greater than 1.

Value

dmscn

returns a vector of density values.

rmscn

returns a matrix of n rows of observations.

Author(s)

Cristina Tortora and Antonio Punzo

References

Punzo, A. & Tortora, C. (2021). Multiple scaled contaminated normal distribution and its application in clustering. Statistical Modelling, 21(4): 332–358.

Examples

x <- matrix(c(0,0),1,2)
alpha <- c(0.8,0.6)
eta <- c(2,4)
density <- dmscn(x = x, alpha = alpha, eta = eta)
density

n <- 100
random <- rmscn(n = n, alpha = alpha, eta = eta)
plot(random)