mixsmsn (version 1.1-10)

faithful: Old Faithful Geyser Data

Description

Waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA.

Usage

data(faithful)

Format

A data frame with 272 observations on 2 variables (p=2)

References

Marcos Oliveira Prates, Celso Romulo Barbosa Cabral, Victor Hugo Lachos (2013)."mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions". Journal of Statistical Software, 54(12), 1-20., URL https://doi.org/10.18637/jss.v054.i12.

Examples

# NOT RUN {
data(faithful)

## Maximum likelihood estimaton (MLE) for the multivariate FM-SMSN distribution
## with generated values
## Normal
Norm.analysis <- smsn.mmix(faithful, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Normal")
mix.contour(faithful,Norm.analysis,x.min=1,x.max=1,y.min=15,y.max=10,
            levels = c(0.1, 0.015, 0.005, 0.0009, 0.00015))

## Calculate the information matrix (when the calc.im option in smsn.mmix is set FALSE)
Norm.im <-  imm.smsn(faithful, Norm.analysis)

## Skew-Normal
Snorm.analysis <- smsn.mmix(faithful, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Skew.normal")
mix.contour(faithful,Snorm.analysis,x.min=1,x.max=1,y.min=15,y.max=10,
            levels = c(0.1, 0.015, 0.005, 0.0009, 0.00015))

## Calculate the information matrix (when the calc.im option in smsn.mmix is set FALSE)
Snorm.im <-  imm.smsn(faithful, Snorm.analysis)

## Skew-t
St.analysis <- smsn.mmix(faithful, nu=3, g=2, get.init = TRUE, criteria = TRUE, 
                           group = TRUE, family = "Skew.t")
mix.contour(faithful,St.analysis,x.min=1,x.max=1,y.min=15,y.max=10,
            levels = c(0.1, 0.015, 0.005, 0.0009, 0.00015))

## Calculate the information matrix (when the calc.im option in smsn.mmix is set FALSE)
St.im <-  imm.smsn(faithful, St.analysis)

## Passing initial values to MLE and automaticaly calculate the information matrix
mu1 <- c(5,77)
Sigma1 <- matrix(c(0.18,0.60,0.60,41), 2,2)
shape1 <- c(0.69,0.64)

mu2 <- c(2,52)
Sigma2 <- matrix(c(0.15,1.15,1.15,40), 2,2)
shape2 <- c(4.3,2.7)

pii<-c(0.65,0.35)

mu <- list(mu1,mu2)
Sigma <- list(Sigma1,Sigma2)
shape <- list(shape1,shape2)

Snorm.analysis <- smsn.mmix(faithful, nu=3, mu=mu, Sigma=Sigma, shape=shape, pii=pii,
                            g=2, get.init = FALSE, group = TRUE,
                            family = "Skew.normal", calc.im=TRUE)
                            
mix.contour(faithful,Snorm.analysis,x.min=1,x.max=1,y.min=15,y.max=10,
            levels = c(0.1, 0.015, 0.005, 0.0009, 0.00015))

## Search for the best number of clusters from g=1 to g=3
faithful.analysis <- smsn.search(faithful, nu = 3, g.min = 1, g.max=3)
mix.contour(faithful,faithful.analysis$best.model,x.min=1,x.max=1,
            y.min=15,y.max=10,levels = c(0.1, 0.015, 0.005, 0.0009,
            0.00015)) 
# }