# Old Faithful Geyser Data Waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA. data ```r data(faithful) ``` ## Format A data frame with 272 observations on 2 variables (p=2) latin1 ## 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. ## Examples ```r ## 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) ``` ## 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.

faithful function