faithful {mixsmsn}

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)

Source

H?rdle, W. (1991) "Smoothing Techniques with Implementation in S". New York: Springer.

Azzalini, A. and Bowman, A. W. (1990). "A look at some data on the Old Faithful geyser". Applied Statistics 39, 357–365.

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)) 

## End(Not run)