TSMNgenerator {TSMN}

Generator of Truncated Scale Mixtures of Normal Distributions

Description

This function generate random TSMN samples from Normal, Student-t, Slash and Contaminated Normal, using the the inverse method.

Usage

TSMNgenerator(n, mu, sigma2, nu = NULL, lower = -Inf, upper = Inf, dist = "Normal")

Arguments

n

Number of observations.

mu

Location parameter.

sigma2

Scale parameter.

nu

Parameter of the scale variable of the SMN family. Must be NULL in case of Normal distribution. Must be a bidimensional vector in case of contaminated normal distribution (CNormal).

lower

Lower bounds.

upper

Upper bounds.

dist

Distribution to be used: "Normal" for Normal model, "T" for Student-t model, "Slash" for slash model and "CNormal" for contaminated Normal model.

Details

For the contaminated Normal distribution, each component of the bidimensional vector "nu" must lie on (0,1).

Value

Returns the sample generated according to the parameters.

Author(s)

Eraldo B. dos Anjos Filho [e-mail] and Aldo M. Garay [e-mail]

Maintainer: Eraldo B. dos Anjos Filho [e-mail]

References

Aldo M. Garay, Victor H. Lachos, Heleno Bolfarine, Celso R. Cabral. "Linear censored regression models with scale mixtures of normal distributions". Statistical Papers, 2017, vol. 58, issue 1, pages 247-278

See Also

TSMNmoments

Examples

## A test sample to compare theoretical and empirical moments, considering the following parameters:

mu = 2
sigma2 = 4
nu = 5
lower = -3
upper = 10
dist = "T"
n = 10000

## Theoretical moments with TSMNmoments
theor<-TSMNmoments(mu=mu, sigma2=sigma2, nu=nu, lower=lower, upper=upper, dist=dist)

## Generate the sample with TSMNgenerator to compute the empirical moments
empir<-TSMNgenerator(n=n, mu=mu, sigma2=sigma2, nu=nu, lower=lower, upper=upper, dist=dist)

## Compare the results
data.frame("1st" = c("Theoretic" = theor$EY1, "Empirical" = mean(empir)),
           "2nd" = c("Theoretic" = theor$EY2, "Empirical" = mean(empir^2)),
           "3rd" = c("Theoretic" = theor$EY3, "Empirical" = mean(empir^3)),
           "4th" = c("Theoretic" = theor$EY4, "Empirical" = mean(empir^4)))