generator {stats4teaching}

Generation of multivariate normal data.

Description

This function generates univariate and multivariate normal data. It allows simulating correlated and independent samples. Moreover, normality tests and numeric informations are provided.

Usage

generator(n , mean = 0, sigma = 1, coefvar = NULL,
    sigmaSup = NULL, dec = 2)

Arguments

n

vector size of samples.

mean

vector of means.

sigma

vector of standard deviations or covariance/correlation matrix.

coefvar

an optional vector of coefficients of variation.

sigmaSup

an optional vector of standard deviations if sigma is a correlation matrix.

dec

number of decimals for observations.

Details

If mean or sigma are not specified it's assumed the default values of 0 and 1.

If coefvar (= sigma/mean) is specified, function omits sigma and sigmaSup. It's assumed that independent samples are desired.

Number of samples are choosen by taken the longest parameter (n, mean, sigma, coefvar). Therefore, function rep is used. Pay attention if vectors don't have same length!

If sigma is a vector, samples are independent. In other case (sigma is a matrix), samples are dependent (following information meanst be taken into account: if sigma is a correlation matrix, sigmaSup is required).

Value

List containing the following components for independent (with the same length) and dependent samples:

• Samples: a data frame containing the samples created.

• Test normality test for the data (shapiro.test() for n <= 50 and lillie.test() in other case).

List containing the following components for independent samples with different lengths:

• X_i sample number i.

Examples

generator(4,0,2)

sigma <- matrix(c(1,0.8,0.8,1),nrow = 2, byrow = 2)
d <- generator(4,mean = c(1,2),sigma, sigmaSup = 1)

generator(10,1,coefvar = c(0.3,0.5))

generator(c(10,11,10),c(1,2),coefvar = c(0.3,0.5))